The mystery of the Trinity

What exactly is the Trinity? How can God be three people at once? Which one should I pray to? And what role does each of the three play? I'm confused./

Terrific questions! The concept of the Trinity is one of the great mysteries of the Bible. Romans 11:34 says, "Who among us can know the mind of the Lord?" God's character is so enormous that we, with our limited minds, cannot comprehend all that he is.

The Bible is clear that God is three-in-one: God the Father, God the Son, and God the Holy Spirit (see Matthew 28:18-20). The three parts are separate personalities. And yet together, they form one being: God.

We can try to explain the Trinity with analogies and illustrations, but even these come up short, because God is so great, no illustration really does him justice.

For instance, look at an egg, and its three separate but equal parts—yolk, white and shell. Each has its own identity and purpose, and yet all three make up something more. Take away one of the three parts, and it's no longer an egg.

Now look at yourself. You probably have three names: a first name, a middle name and a last name. Standing alone, each of those three names represents you, but none of the three names alone represents your whole name. Only all three names together can do that.

Who do you pray to? God the Father. In Matthew 6:6, Jesus says, "But when you pray, … pray to your Father, who is unseen." Then Jesus went on to tell us how to pray, starting out with the words, "Our Father in heaven … "

You also asked about the roles of all three persons of the Trinity. Here's a brief, though not complete, look:
God the Father's role is to generate things. Things originate with him and flow from him. God the Father is equal with the Son and the Holy Spirit, but things start with him. The Father sent both the Son (John 3:16-17) and Holy Spirit (John 14:26) into the world.
God the Son's role is to pay for our sins with his blood, which he did on the cross (Romans 5:9). The Son also acts as a lawyer for us before God, acting as a "mediator" between us and God (1 Timothy 2:5), and speaking "to the Father in our defense" (1 John 2:1).
God the Holy Spirit has many roles. The Spirit helps us pray (Romans 8:26-27). He gives us new life (John 3:3-6). He is our Comforter, and he helps us understand God's word (John 14:26). He lifts up Christ (John 15:26). He convicts us of sin (John 16:7-11). He helps us to live holy lives (Romans 15:16). He gives us love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self-control (Galatians 5:22-23). He helps us share our faith (Acts 1:8). And he lives inside us (Romans 8:11).

These things are just a beginning. We can't fully "define" God, or the Trinity. But that's what's so cool about God. He's so awesome, powerful and inexplicable, that we can't define him. Nor would we want to. He just leaves us looking to him with wonder and awe.