Where did the idea of the Trinity come from?

The revelation of scripture which describes God as existing as one being, with three distinct persons, does not hinge on any particular verse, but is gradually revealed from Genesis to Revelation.  If 1 John was removed from the Bible it would have no impact on the concept of the Father, Son and Holy Spirit, as three distinct persons of the only God. The word Trinity is just a catch word to say Father, Son and Spirit, assuming that only the Father, Son and Spirit are eternal and without any boundaries, being infinite in all their qualities and essence. The Son had no beginning, the Spirit had no beginning, the Father had no beginning and they are the one and only God. All other things that exists, we're the creation of the triune God.  These many Biblical truths are stuffed into the word 'Trinity' as a container for what the Bible clearly teaches.

In the creation of all things, the Trinity manifests that each person of the Trinity has a distinct operation in their relation to the other persons. When the Bible refers to ‘God’ in general, then no particular person of the trinity is being identified, so we just can know it means all three.  However, when any special impression is made of the special works or properties, more specific to one of the persons of the Trinity; then the Bible is drawing attention to that work as assigned peculiarly to that person.   For example, in the creation (creation = all that is not God) the 'original will' behind the creation, is an expression of the Father.  Gods powerful 'word' in the creation, is an expression of the Son. The 'perfecting and finishing' works of creation is an expression of the Spirit.

One quick proof of the Trinity might therefore go like this:

Originally in the shadows of the obscure revelation under the Old Testament there was only God.  God is, God the Father, Son and Holy Spirit, but not yet known in that full developed sense as we know today. Only known in a weak dark shadowy sense, under the natural and gradual progression of revelation.

We actually see all three persons at work in the creation, but only obscurely:

In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. And God said, “Let there be light,” and there was light. (NIV Genesis 1:1-3)

Yes, we do see the Father 'speaking' his original will, we see his 'word' powerfully creating, and we see the Spirit, perfecting and completing the work as it hovers, but this may easily be viewed as just God, who hovered over the waters, not the trinity.  We know it is clearly the trinity looking backwards with our light that we now have, but it can't be said to be so clear at first.

So how did we get our clear view? Well first there was the Promise of a 'Messiah', then a Temple for the 'Spirit' in the Jewish nation.  The promise for a Messiah is a theme that developed over a long period with certain immersing concepts until he finally came.  One of these central themes regarding Messiah is that he would be a Son. He would've a Son of David, but also a Son born of a virgin, 'God with us'. This is getting clearer for sure, but still not fully clear.  Once the Son arrived then it was clear. jesus clearly distinguished between His 'Father' and the 'Spirit'.  This is how the trinity became clear, Christ taught it and was the clear manifestation of one of its persons.

First he was manifested as the Son at the inauguration of his ministry:

As soon as Jesus was baptized, he went up out of the water. At that moment heaven was opened, and he saw the Spirit of God descending like a dove and alighting on him. 17 And a voice from heaven said, “This is my Son, whom I love; with him I am well pleased.” (NIV Matthew 3:16-17)

Then besides proving his divinity from his power over disease, devil and nature he directly made known his divine per-existent state through argumentation:

Jesus replied, “If I glorify myself, my glory means nothing. My Father, whom you claim as your God, is the one who glorifies me. Though you do not know him, I know him. If I said I did not, I would be a liar like you, but I do know him and obey his word. Your father Abraham rejoiced at the thought of seeing my day; he saw it and was glad.”  “You are not yet fifty years old,” they said to him, “and you have seen Abraham!”  “Very truly I tell you,” Jesus answered, “before Abraham was born, I am!” (NIV John 8:54-58)

Of course I AM was the name God (Father, Son and Spirit) gave himself to Moses which means 'always existed'.

Now we have the foundation of The Father and The Son, all we need is the Spirit to complete the revelation. 

Jesus made it clear the Spirit was not the Father:

But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you. (NIV John 14:26)

But we already saw in Genesis, the Spirit was involved in creation and in the Temple the Spirit dwelled, so as the Spirit is the pre-existent God and 'not the Father', then all three, Father, Son and Spirit are God.  These three are therefore put on the same level, so that when we are made to join in the gospel and in Christ, we are being joined into God, which means all three:

Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit. (NIV Matthew 28:19)

Therefore, now that we have the full knowledge of Christ, we can look back and realize things they never saw clearly before. 

In the past God spoke to our ancestors through the prophets at many times and in various ways, but in these last days he has spoken to us by his Son, whom he appointed heir of all things, and through whom also he made the universe. The Son is the radiance of God’s glory and the exact representation of his being, sustaining all things by his powerful word. After he had provided purification for sins, he sat down at the right hand of the Majesty in heaven. (NIV Hebrews 1:1-3)

'Many times and in various ways' indicates the imperfection of how he spoke in the past. Before it was alike a spark, here and there, but now a radiant Sun! 

Why could the Trinity not be so clearly seen before Christ? Well simply because everything in the days of the Law were faint, weak and dim.

The law is only a shadow of the good things that are coming—not the realities themselves. (NIV Hebrews 10:1)

By calling this covenant “new,” he has made the first one obsolete; and what is obsolete and outdated will soon disappear. (NIV Hebrews 8:13)

Therefore although the Trinity first came from Genesis Chapter 1, it never became clear until the Son was revealed.