First of all, Christians don't believe in three Gods. That's a heresy called Tritheism. Second, we don't believe that the Father, Son, and the Holy Spirit are three "forms" of God—like, steam, water and ice. That's the heresy called Modalism. Third, we don't believe that the Father, Son, and Holy Spirit are "parts" or "pieces" or God. That would imply that Jesus is 1/3rd God, the Father is 1/3rd God, and the Holy Spirit is 1/3rd God.

B. Where do we find this doctrine in the Bible?

I would answer that the Trinity is taught in both the Old and the New Testaments. It is taught by implication in the Old and by direct statement in the New.

For instance, the Bible contains numerous clear statements regarding the unity of God: Deuteronomy 6:4 tells us that "the Lord is one." 1 Corinthians 8:4 adds that "there is no God but one." 1 Timothy 2:5 explicitly says "there is one God." All Christians heartily affirm this truth.

However, the Bible also contains clear statements regarding diversity within that unity. For instance, in the very first verse of the Bible we are told that "In the beginning God." The Hebrew word for God is elohim, which is actually a plural form of the word el. It's a word that in other contexts is sometimes translated as "gods," referring to heathen deities. Later in the same chapter we have one of the most striking statements of diversity-in-unity:

Then God said, ‘‘Let us make man in our image, in our likeness, and let them rule over the fish of the sea and the birds of the air, over the livestock, over all the earth, and over all the creatures that move along the ground." So God created man in his own image, in the image of God he created him; male and female he created them. Genesis 1:26-27

Notice the shift in pronouns. "Let us … in our image … So God created man in his own image. … he created him." From us and our to he. Why the shift? Commentators speak of a literary form called the plural of majesty or the "editorial we." This much is certainly true. If Genesis 1 does not explicitly teach diversity-in-unity within the Godhead, it certainly leaves room for it to be developed later in the Bible.

Isaiah 48:16 seems to explicitly refer to all three Persons of the Trinity (with my additions in parentheses): "And now the Sovereign LORD (the Father) has sent me (the Son), with his Spirit (the Holy Spirit)." I'm not suggesting that Isaiah fully understood the Trinity or that the Jewish readers would have understood what it meant, but I do think that in the light of the New Testament, we can say that this seems to be a clear statement of the Trinity in the Old Testament.

Consider further this line of evidence. All Three Persons are called God in different places in the Bible.

Father — Galatians 1:1 

Son — John 20:28 

Spirit — Acts 5:3-4 

How could the Son and the Spirit be called God unless they somehow share in God's essence? But if they share in God's essence, they are God alongside the Father.

Finally, all three Persons are associated together on an equal basis in numerous passages:

Jesus' baptism—Matthew 3:13-17 (voice of the Father, Son baptized, Spirit descending like a dove). 

Salvation—1 Peter 1:2 (chosen by the Father, sanctified by the Spirit, sprinkled with the blood of Jesus). 

Sanctification—2 Corinthians 13:14 (grace of the Lord Jesus, love of God, fellowship of the Holy Spirit). 

Christian Baptism—Matthew 28:19 (baptized in one name, yet three Persons—Father, Son, and Holy Spirit). 

Prayer—Ephesians 3:14-21 (strengthened by his Spirit, know the love of Christ, filled with the fullness of God). 

Christian Growth—2 Thessalonians 2:13 (chosen by God, loved by the Lord, sanctified by the Spirit). 

This list of passages might be extended. It simply shows how easily the writers of Scripture passed from one Person of the Trinity to another, doing so in a way that assumes their equality of nature while preserving their distinct personhood. If the doctrine of the Trinity is not true, it would seem to be blasphemy to speak so freely of the Father, the Son, and the Holy Spirit in one and the same breath.