Read Genesis 1 where God says “let US make man in OUR image”. Then you also read that the Spirit of God was moving across the face of the waters.
You have in the clearest possible terms the existence of more than one “person” being God, and at least one of them is the Holy Spirit, right from the start.
In John 1 you read that Jesus was the one through whom all the world, and indeed, all the universe was created. Jesus used the name “I AM” in speaking of his pre-existing Abraham. Moses spoke to “I AM” recording that he spoke to God. Paul in Hebrews 11 writes that Moses esteemed the reproach of CHRIST of greater value than the treasures of Egypt. Revelation tells us that the Lamb is worthy of worship, and we know that only God is worshipped. All these, and many more, indicate that Jesus is God.
I am assuming no one needs convincing that the Father is God.
So we can clearly see all three are God.
How are they three and also one? If we could understand God, if who and what and how and when and where were fully comprehensible to us, He would not be God.
A comment is that I am relying on John 1 too much and that it is being misread, misquoted and/or misunderstood. This I disagree with. The idea of John 1 not referring to Christ being God is also a Jehovah's Witness belief and they raise the same objection. They refer specifically to verse 1 saying that it should read "In the beginning was the Word, and the Word was with God, and the Word was a God".
This translation, by changing it to "the Word was a God" is a dishonest translation, for that concept is not found in that verse in any way shape form or hint.
The opening words of John echo the exact words of Genesis 1:1 in the Septuagint, but draws a special emphasis to pre-existance by inserting "was" (ēn). The readers to whom he wrote would have been intimately familiar with the Septuagint, because as some do not immediately realise, to the New Testament world, the Old Testament, and the Old Testament only, was the Bible. The New Testament was being written in their time by men who walked among them. They duly respected their writings as the writings of Apostles, but as Paul writes of the Bereans, "they were more noble" in that they "searched the scriptures daily" to confirm that what he wrote, "was so". By this, Paul meant, they searched the Old Testament writings to confirm his gospel.
Genesis 1:1 in the Septuagint states "en archē ho Theos" and John 1:1 writes "en archē ēn ho Logos". The emphasis there to draw attention to the preexistence of the Word, saying that be existing before any creation, he is God, not "a" God. The Bible had to this point only ever said this "in the beginning (en archē)" of only one, and that one is God.
These opening words "in the beginning was (en archē ēn)" from John is to emphasise to his readers in an implicit and powerful way that the preexistence of the Word necessitates the deity of the Word. This he says explicitly later to remove all possibility of doubt.
Not satisfied with only pointing out that the Word preexisted creation, John makes it clear that at creation the Word was not elsewhere, but that the word was intimately connected with God - "and the Word was with God. (kai ho Logos ēn pros ton Theon)". This we can translate better. "and the Word was with THE God" which is the original Greek. A clear indication that he is not speaking of principalities and powers but that He speaks of "the creator God" which inanimate creation obeys and through whom it is formed.
Now, not satisfied with all the preceding, but building on it, John explicitly states "and the Word was God (kai Theo ēn ho Logos)". But here is where everyone differs, not least the Jehovah's Witnesses (noted JW from now on).
The Greek writes literally "and God was the Word".
Let's re-read with that translation (Greek at that time had only uncials (capital letters), but in our modern text word that is synonymous with SHOUTING so I'll do the opposite):
"in the beginning was the word and the word was with god and god was the word"
Now the question to decide is which is correct? This is what JW's translate as "the word was a god".
I see the exact opposite. In fact, this is the strongest statement in support of the Trinity doctrine. John speaks of the Word's preexistence prior to creation, he indicates the Word was separate but associated with God, and then he says God is the Word. Yes, indeed, I prefer to read "the Word was with God and God was the Word." John here says exactly what Trinitarians say "The word is separate from God but the Word is not separate from God". In a way which human language is not designed to describe John describes "that holy thing" as something individual but not individual. As combined but separate. As One but not One.
In the 1st chapter of John though we find elsewhere the clear indication that Jesus was the one through whom all creation was made. Now when we look at Genesis we clearly find that God created the world. Is so many many ways in this chapter, John clearly points to the divinity of Jesus.
I suppose, in the end, a large part of this discussion on the Trinity also revolves on the discussion "is Jesus God" just like I am informed Gnostics need to discuss "is the Father God".
My original pre-edited answer does that in some detail but I will add more:
Who can forgive sin, but God?
Who has authority to state you will be in paradise with me, but God?
Who other than God can be the resurrection and the life?
God alone accepts worship - Jesus accepted worship. Angels (created beings) quickly admonish worship aimed at themselves and instruct - Worship God!
And He said to me. "It is done! I am the Alpha and the Omega, the Beginning and the End. I will give of the fountain of the water of life freely to him who thirsts. He who overcomes shall inherit all thing, AND I WILL BE HIS GOD and he shall be My son.
Jesus is Wonderful, Counselor, Mighty God, Everlasting Father, Prince of Peace.