No, Christians don't worship three Gods; there is only one God, and He alone is the One we worship and serve. When Jesus was asked which of the commandments was most important, He replied, "Hear, O Israel, the Lord our God, the Lord is one" (Mark 12:29).
The Bible does tell us, however, that God has shown Himself to us in three distinct ways. First, He has shown us that He is our Father. Like our earthly fathers (but in a far greater way), He brought us into being, and He loves us and protects us and takes care of us. The Bible says, "As a father has compassion on his children, so the Lord has compassion on those who fear him" (Psalm 103:13).
But God also has shown Himself to us in the person of Jesus Christ, who was God in human flesh and came to earth for a distinct reason: to make it possible for us to be with Him in heaven forever. Our sins separate us from God -- but by His death on the cross, Jesus Christ became the complete sacrifice for our sins. God also comes to us in a third way -- by His Holy Spirit, who lives within us when we put our faith and trust in Christ.
Just as a clover has three leaves and yet is still one clover, so God has three "personalities" -- and yet is still one God. And through each of these God shows His love for us. May you respond to His love by giving your life to Him -- Father, Son, and Holy Spirit.