3-days metro bus ticket for Paris

You can find all of this information on the dedicated page on the RATP website. RATP is the public transport company which handles Metro, Bus, Regional Trains (RER), in Paris.

In your case, it would seem that the Paris Visite pass is what you are looking for:

How does it work ?

The Paris Visite travel pass allows you to use all of the public transport networks: the metro, tramway, bus, RER and SNCF Transilien networks.

Valid for 1, 2, 3 or 5 consecutive days, the pass allows you to travel anywhere in Paris (zones 1 to 3) or in Paris and the Île-de-France region (all zones, including airport connections, Orlyval, Disneyland Paris and Château de Versailles).

At the time of writing, the prices are 26,65€ for three days of travel within zones 1-3.

Your options (this is an FAQ, but I'm making a new answer that's updated for 2022 — the main change is that paper tickets are gradually being replaced by electronic passes):

• Navigo Découverte pass (5€), plus a weekly pass: 22.80€ for Monday–Sunday (it can only be a calendar week, not an arbitrary 7-day period, and needs to be bought on Thursday at the latest), valid for the whole region. Note that you must stick a passport-sized photo onto the pass; I don't know how that works with a phone. Typically the best value if your stay fits within a calendar week (it's a commuter-oriented pass and those are rather cheap).
• Navigo Easy pass (2€), plus separate tickets: t+ tickets (14.90€ for 10 tickets, 1.90€ for a single ticket; you can also put Orlybus and Roissybus tickets on the pass). Each t+ ticket is valid for one bus/tram trip (including transfers within a reasonable time limit, but not return trips even within the time limit) OR one metro trip (with transfers as long as you don't exit the metro, including RER inside the Paris city limits but not RER to e.g. La Défense, Versailles, etc.) OR one trip on the Montmartre funicular. Transfers between bus/tram and metro/RER consume separate tickets (there's talk of allowing free transfers but currently that's only the case if you have a resident's pass). Train and RER travel in the suburbs require paper tickets for now. This is typically the cheapest option if a commuter pass doesn't work for you or if you're not going of the city, unless you end up with many tickets left over from a pack of 10.
• Navigo Easy pass (2€), plus days passes: 7.50€ for one day for just Paris, 12.40€ including Orly and Versailles, 17.80€ including Roissy and Disneyland. A day is a calendar day, not an arbitrary 24-hour period. Short-visit passes are relatively expensive unless you're going to suburbs that require a train plus a bus.
• Paris Visite, the tourist pass. 26.65€ for 3 days for just Paris (zones 1–3), 53.75€ for 3 days for the whole region. Other durations exist. The pass gives you small discounts to a few tourist attractions. Almost always more expensive than other options.

Vending machines take cards and coins (exact change not needed), but not banknotes. You can buy tickets with banknotes (and get change) at some shops. You can also charge a Navigo Découverte/Easy pass with most NFC phones. If you have a compatible phone, you don't need a physical pass at all — but currently only phones with Samsung Pay are supported.

In any case:

• Passes are valid for almost all public transport inside the chosen zones (buses, trains, trams, funicular). Notable exceptions are Orlyval, private airport coaches (“Le Bus direct”, Beauvais airport coaches), and sightseeing buses and boats.
• Almost everything that a tourist would want to see is in zone 1 (Paris city limits), except Versailles (zone 4) and Disneyland (zone 5). La Défense is in zone 3. Orly airport is in zone 4, Roissy airport is in zone 5, and Beauvais airport is outside the Paris region.
• Children under 10 pay half fare. Children under 4 ride for free.

Note that the metro means stairs everywhere. They're usually not very long, but any amount of stairs can be inconvenient with a stroller or heavy luggage, let alone with reduced mobility. If you're alone with a stroller, locals will readily help you (but you may have to ask explicitly, as Parisians tend to hurry and mind their own business). Locals tend to be less helpful with luggage, but given the crowds chances are good that someone will help. Crowding can be a problem during the morning and evening rushes when all the trains and buses are jam-packed. Few stations have an elevator. All buses are wheelchair accessible, at least inside Paris (I think not in all suburbs yet).