No, Christians don't worship three different Gods. They worship only one God - because no other deity exists in addition to Him. The Bible says, "Take to heart this day that the Lord is God in heaven above and on the earth below. There is no other" (Deuteronomy 4:39).
It's true, however, that the Bible tells us that Jesus is also God, and the Holy Spirit is also God. How can this be? Theologians have pondered this for centuries, and I admit that it's not easy for us to understand. (In fact, we'll probably only understand it completely when we get to heaven.) But this much is clear: God has shown Himself to us in three ways - as Father, Son and Holy Spirit. Each has a separate function - and yet they are all united as one God.
Let me illustrate it this way. Have you ever thought of some of the things we see around us that are both three - and yet also one? Centuries ago, St. Patrick used a clover leaf to teach the Irish about this - it has three leaves, and yet is still only one leaf. Or think of water. A quart of water can be ice, water, or steam - but it's still the same quart of water.
Don't get bogged down in questions like this, however. Instead, open your heart to Jesus Christ and make Him the ruler of your life. God loves you - and He loves your neighbor also. May you both discover the joy of knowing Him.