Flying in a British bomber during World War Two was one of the most ... Early in the war bomber pilots were taught terrible lessons about ... They were worse really than flak because you didn't see that until it actually burst. ... Occasionally, planes might even be hit by bombs released from a plane above.

If there's a visible landmark at a known distance & angle from the target ( Sometimes this is called the IP - initial point.) then at a known speed you should be over the target at speed/distance seconds after passing it. Is that what you're thinking of?

Like all the other methods though it depends on accuarately knowing the speed and distance, and then there's other factors like wind, air density...

After the nice answers above about bombers, here a humbler answer about how to bomb with a P-40 fighter, from John Vader's book "P-40".
Problems:

• crew is just fighter pilot, no bombardier or bomber optics at all.
• Actually, at the right time to drop the bomb, the target is invisible, as there are no glass window looking down. And the target has been invisible for some time.
• The plane can dive, but not as well as a dive bomber. If you try to dive as a Stuka, you can not recover from the dive and crash in the ground.

It requires some practice with dumb bombs, but USA pilots developed this technique at the Pacific front:

1. Dive at ~45 degree, pointing at the target with your target sight. Do not keep it on the sight, let his image go "down"
2. Wait until the target disappears from your view, under your plane
3. Count one number for each 300m of altitude. e.g, if you are at 600m altitude, count up to 2.
4. Get out of the dive, when the plane is almost leveled up, drop the bomb.

Obviously this is not accurate but: a) not-so accurate incendiary bombs may still be useful when bombing an enemy base; b) they usually would bombs enemy vehicle convoys using squads of P-40. After all 4 planes dropped bombs, they would come back to strafe them with their .50. Even if some bombs missed, that is not so critical.

The other option was to fly horizontally, at 20m altitude, right at the top of the trees, and drop bombs just above the enemy. But this is more dangerous.

PS: both approaches also work with plane simulators or games such as Warthunder. After some practice to learn to keep track of altitude and dive angle, it was nice to bomb an enemy tank from a P-40 after counting up to 2...

The bomb sights as mentioned in the other answers provided the last stage of targeting: they assume the bomber is in the general area of the target and are used to decide when exactly to drop the bomb load.

Getting to the target area was a problem too. Navigation was commonly done by looking at the ground and comparing to the map (by day) or the use of a sextant (by night). These methods were imperfect to the point where occasionally, the wrong city was bombed.

In WW2, other methods were devised to make navigation easier. Radio navigation was one: radio transmitters in friendly territory sent signals that could be received by the bombers, giving a distance or heading from the transmitter (and thus a location).
Initially only a few aircraft in the formation would have radio navigation. These would guide the rest of the formation. Examples are Gee and Oboe. These got good enough to get the bomber within a few hundred m of the target, and bombing (well, carpet bombing at night) could take place without using a bomb sight.

computing technology wasn't advanced enough to calculate when to drop bombs accurately on a target

Accuracy was of course the paramount issue, however computing technology was used to improve accuracy. Just not the specific type of computer technology you may have in mind (e.g. specifically digital not analogue, specifically electronic not electromechanical)

The bombsight that resulted was the Mk XlV regarded then as the wonder sight of the day. It was designed to enable the run up to the target flying straight and level to be restricted to a mere ten seconds and enable the pilot to carry out evasive manoeuvres on his approach to the target. It could be used to bomb both on the climb and the glide. The bombsight consisted of a computer cabinet mounted to the left of the Air Bomber and a stabilised sighting head with optical graticule. The sight was one of the first practical uses for a mechanical computer and Babbage would have been proud of it.

Source: Henry Black, Lancaster Archive

bomber pilots using a modified watch to deploy bombs.

Bombsights were not made by taking a watch and modifying it. They were not used by pilots in most cases.

This question depends on how bombers were used. The British and Germans utilized night time bombing missions so visual bomb sights were not as useful to them. They both opted for radio beam technology which both guided their bombers to the target and informed them when to drop their payloads. The Germans used this technology from the beginning of the war in 39, the British while always flying night time missions converted to their own brand of beaming technology later in the war. The United States philosophy was to defend their bombers in the air, and fly daylight missions which they felt were more accurate and reliable in hitting the target. The United States tried different strategies to defend their bombers in daylight before settling on long range fighter escorts with extra large drop tanks.

The problem everyone was trying to counter was Bombers were slow vulnerable cumbersome beasts, vulnerable to fighter intercepters. This vulnerability was negated by night time bombing. Even large slow moving bombers could fly safely across Europe or the UK with a coat of dark paint and a sufficiently high altitude. Problem was such high flying nighttime missions while safer for the bombers were not very accurate at hitting targets smaller than cities, and even cities proved difficult when they were blacked out. Which meant nighttime bombing without electronic aids was largely a terror weapon, not a strategic weapon.

Germans

To negate this shortcoming, the Germans used sophisticated radio beaming technology. First the Germans used a system called Knickebein. One beam would determine the path of the bombers. If the bombers were to the right or left of the beam, radio's in their pilots ears would inform them with a series of dots(turn right) or dashes (turn left). An intercepting beam would tell the bombers when to drop their bombs. The British code named the German knickebein system "head-ache" and their countermeasures were code named "aspirin". The British struggle to identify and counter this German system was known as the "Battle of the Beams".

The knickenbein system had a number of short comings. The beam was relatively easy for the British to identify once they started looking, and the system was not designed to direct large formations. These shortcomings were addressed when knickenbein was replaced by the more accurate, better ranged, and harder to detect X-Gerät system, which also used Radio beaming technology. X-Gerät used a more focused beam which was more difficult for enemy countermeasure craft to find. More focus also meant more accuracy.

British

The British adopted similar systems to the German Knickenbein and X-Gerät systems which also relied upon radio beaming technology(Gee and Oboe).

Encyclopedia Britanica
From late 1943 the RAF used two radar-beam systems called Gee and Oboe to guide its Lancaster and Halifax bombers to cities on the Continent. In addition, the bombers carried a radar mapping device, code-named H2S, that displayed reasonably detailed pictures of coastal cities such as Hamburg, where a clear contrast between land and water allowed navigators to find the target areas.

United States

The United States was not a fan of night time bombing. While safer for the bombers, prior to the development of allied beaming technology night time bombing compromised the accuracy and effectiveness of the missions. They opted instead to use a sophisticated bomb sight which relied upon visual markers to determine the plane's true ground speed, and then mechanically adjust the targeting apeture to account for altitude and speed. This device was named the Norden Bombsight. The Norden bombsight was pretty accurate in ideal conditions, but was subject to problems from rain, fog, or cloud cover all of which could be sufficient to scrub entire missions. The Norden Bombsight was also notoriously complex and difficult to use.

An additional benefit of American daylight missions was that the allies could conduct missions 24 hours a day, with the RAF conducting night time raids. The United States used the Norden Bombsights in both theaters of WWII, Korea and Vietnam. Both nuclear devices dropped on Japan were dropped utilizing the Norden Bombsight.

To counter the vulnerability problems of bombers the Americans first tried to fortify its bombers. The theory was fortified bombers in tight formations would be able to defend themselves from enemy fighters. Fortifying the bombers though made them heavier and slower; ultimately this tactic was not effective in countering the dangers of enemy fighters.

P-51 Mustang
In fall 1943, the 8th Air Force's heavy bombers conducted a series of deep-penetration raids into Germany, beyond the range of escort fighters. The Schweinfurt–Regensburg mission in August lost 60 B-17s of a force of 376, the 14 October attack lost 77 of a force of 291—26% of the attacking force. Losses were so severe that long-range missions were called off for a time until an effective escort could be found.

The P-51 mustang with an extra large 80 gallon drop tank would become the bomber escort the United States were seeking. It saved both the American concept of daylight bombing and for that matter the utility of the Norden bombsight with it's ability to protect daylight missions.

Precision strategic bombing has been covered. Here's a few notes about precision tactical bombing, particularly naval targets.

Horizontal bombing, flying in a straight line at high altitude and dropping bombs at just the right moment, proved totally unable to hit moving ships at sea. Even for a non-maneuvering ship, the accuracy simply wasn't there. A level bomber must take into account the velocity vector of the ship (which can change as it maneuvers), the height of the bomb at release, the horizontal velocity vector of the bomb at release (which is the same as the horizontal velocity vector of the bomber), and the effect of wind and drag on the bomb as it falls. This evolving four-dimensional problem (3 spacial dimensions, plus time) is too much for a bombardier to do in their head, or with a simple analog computer, under combat conditions.

Instead, dive bombing proved effective. This simplifies the problem by literally pointing the aircraft straight at the target in a very steep dive. The bomb is released as low as possible to have as short a travel time as possible (5 to 10 seconds) giving the target as little time as possible to maneuver. Being released near vertical, the bomb will go in nearly a straight line to the target simplifying the aiming process. This turns the 4 dimensional problem into a mostly 2 dimensional one: point your nose at the target, hold the dive for as long as you dare, release, and pull up.

This technique also allowed the dive bombers to approach at high altitude, where they were safer, but attack and low altitude where they were more accurate. High attitude bombers are harder to spot, being further away they appear smaller, and can possibly concealed by clouds and the Sun. If the defending Combat Air Patrol is caught at a low altitude or out of position, as happened famously at Midway where the Japanese fighters were just finishing slaughtering low-level torpedo bombers when the dive bombers appeared, they may not be able to climb to attack in time.

It required special training and it required special aircraft. Dive bombers were designed to take the stresses of high speed, and high Gs. Pulling out of a dive on a lesser aircraft could damage the airframe. The steeper the dive, the more accurate the bomb. Aerodynamically, they had to dive in as close to a straight line as possible with no lift to mess up their aim; not generating lift at high speed is what aircraft want to do, so this could otherwise degrade performance.

Dive bombers had some aids. The dive angle could be indicated by a proper artificial horizon, or by the simple expedient of painting angles on the pilot's window and comparing that with the horizon.

Pilots would train to dive at a certain angle, 70° for US naval dive bombers in WWII, and release at a certain airspeed and altitude. This again simplified the calculations. Rather than working out how the bomb will behave for various variables, they could practice and memorize just one particular angle, airspeed, and altitude. Then combat was a matter of following their training.

See Also

• SB Dive Bomber - globalsecurity.org

Different technologies for different aircraft.

• The most primitive aircraft then in use would bomb on unaided eyesight and gut feeling. With dense cloud cover, this could become dead reckoning with compass, airspeed indicator, and watch. Not efficient, but sometimes better than bringing the bombs home.
• Somewhat more advanced aircraft had optical sights, which could be adjusted for altitude, speed, and guesstimated wind over the target. This was used for many daylight attacks. These optical bombsight could get pretty complicated, as in the famous Norden bombsight.
• Late in the war there was radar to detect ground targets, which also worked at night and in bad visibility.
• A somewhat related development was bombing on radio navigation, where the transmitter was in friendly territory on the ground.

But I think you may be remembering the intervalometer do drop a series of bombs after the bombardier selected the initial target. This spreads the load of a single bomber over a larger area.

With the Allies, two methods were used.

The USAAF focused on precision daylight bombing, using the Norden bombsight. This was a mechanical computer that also took control of the aircraft controls -- the bombardier was actually flying the bomber with the bombsight during the final bomb run. Supposedly, the Norden bombsight could factor in altitude, ground speed, and (if it could be ascertained) wind speed. In practice, accuracy wasn't all that great.

The British practiced night area bombing, with bombs being aimed on flares released by pathfinders... aircraft that preceded the main bomber force that dropped large colored flares indicating the aim point. If anything, the British bombing was less accurate than the US bombing, but the British were focused on destroying cities with area bombing.

Both the British and US air forces made up for the relative inaccuracy of their bombing with numbers... major bombing raids would employ several hundred bombers.

Addendum: early in the war, the Germans developed a night time navigation system that involved two precision radio beams that would intersect over the target. Those beams, known as Knickebein, became what was called The Battle of the Beams. The British detected those beams, and developed countermeasures to bend them off of the target. Knickebein was really only truly successful once: the raid on Coventry on 14 November, 1940, that destroyed a substantial portion of the city.

Germany did develop a couple of early guided bombs, the Fritz X and Henschel HS293. These were quite accurate when employed, but required the bomber to visually guide the bomb to the target... which became almost impossible when the Allies controlled the airspace over the potential targets.

Both Germany and Japan made extensive use of dive bombers, which were fairly accurate, albeit somewhat dangerous to the bomber crews, and required numerous small bombers with limited bomb carrying ability. A primary reason the Heinkel 177 heavy bomber failed was a requirement that it be able to dive bomb, which affected the design and resulted in a less than successful level bomber.

Japan did develop one accurate bomb, the Okha piloted bomb. It failed to make a serious impact for the same reason the German guided bombs did not succeed... the Okha had a fairly short range, and required a bomber to deliver it close to the target, at a time when the US Navy had complete control of the air over potential targets.

Precision guided bombs, as we know them today, did not appear until around 1971-1972, at the end of the Vietnam war, and weren't really employed in any great number until the first Gulf War of 1990.

Electronic computing was not available, but a simple and constrained problem like timing a bomb drop can be handled by a dedicated mechanical or electromechanical device, the bombsight. These are "analogue computers," as compared to modern digital computers. They aren't re-programmable, and can only solve the problem that is built into them, but they can be built with much less advanced technology.

For high-altitude bombing, the bombsight was used by a specially trained crewman, the bombardier (US usage) or bomb-aimer (British usage). As the aircraft approached the target, he would set up the bombsight with information such as the altitude, wind speed, type of bombs and so on. He would look through the device's telescope for an aiming mark on the ground and set that. Then he'd either give the pilot directions to turn left or right, or for the more sophisticated devices, the bombsight would tell the bomber's autopilot what to do. The bombsight indicated when the bombs should be released, and he'd push the button to let them go.

In the US daylight raids, formation bombing was often used. A group (3-4 squadrons) would fly in tight formation. The bomb-aimer on the lead aircraft would aim and drop, and all the other aircraft would release when he did. This seems to have been intended to get the most out of the most talented bombardiers. The British night bombers all aimed individually, since formation flying was impractical at night.

Models of bombsight included the US Norden and Sperry bombsights, which were aided by Sperry autopilots. The British used the Mark XIV for night bombing, and the SABS for special daylight tasks.

Low-level bombing generally used simpler sights. One British example was the Low Level Bombsight Mark III, intended for operations over the sea. The simplest kinds of bombing, such as dive- or skip-bombing were aimed by the pilot, using a simple sight.

I've avoided the term "precision bombing" this far, because it was the subject of a lot of controversy at the time, and ever since, and gets into political and doctrinal matters, outside the scope of this question.

As well as visual bombsights, there were a variety of radar- and radio-based systems for helping with bombing.

• The simplest was a ground-mapping radar, such as the H2S system. These didn't appear until early 1943, by which time the American and British fleets of heavy bombers were growing fast.

• The Gee system was a radio navigation system that was accurate to a few hundred yards at 350 miles (limited by the curvature of the Earth hiding its ground stations in the UK). This was good enough for area bombing without a bombsight (and hence through clouds), and when you wanted better precision than that, it at least made sure you were in the right area.

• The Oboe system required both-ways communication between ground stations in the UK and a single aircraft (again, limited by the curvature of the Earth), but it was accurate to around 50 yards, approaching the accuracy of modern civilian GPS. It was used by "Pathfinders," squadrons whose job it was to mark targets with flares. The main body of bombers would aim at the flares.

• The Gee-H system was a kind of "reverse Oboe" in that the large control system on the ground in the UK had been miniaturised and was fitted in bombers. About 80 aircraft could use it simultaneously. Its accuracy was about 150 yards.

The Germans tried hard to jam and mislead all of these electronic systems. The reason that all of them are British is that the British operated at night, and needed them to find targets.

The Americans used ground-mapping radar to bomb through clouds, but the other devices were less necessary in daylight, and they don't seem to have used them much. Their radars were H2X which was developed from H2S, AN/APQ-13 and AN/APQ-7. The numbers weren't assigned in the order they entered service. Add-ons to connect them to the Norden bombsight were available just after the end of the war in the Pacific.