Hi Nathan,
I am so glad you came to the realization that God exists. The only way to experience a total relationship and the inner peace you are looking for, is through his son Jesus Christ. He sent his son Jesus to die on the cross for us in order to restore our (man's) relationship with him. The bible tells us there is no other way, whereby we may be saved.
There is no formal way to approach Jesus. He looks directly at the heart. The bible says that if you believe in your heart that Jesus is the son of God and confess with your mouth that God has raised him from the dead, thou shall be saved. Once a person becomes saved, they experience total peace and joy. When you talk to him be honest and confess the things that are in your heart, you will be surprised at the changes that will come about in your life.
The prayer below is a stepping stone in case you are lost for words. When you pray it, just be sincere and mean it from your heart.
Jesus, I know I am a sinner and can't save myself. Thank you for dying on the cross to pay the penalty for my sin. I receive you as my savior and Lord. Take control of my life and make me the kind of person you want me to be.
The next step would be to study your bible. The bible tells us to study to show ourselves approved. There is strength in the word of God. It is food for the soul. Another good reason to study, is that no one can deceive you, because you have first hand knowledge of the word for yourself. Plus you will learn the history of creation and the power of our God. Find yourself a bible believing church where you can worship, grow and fellowship with other believers. God will do the rest. Your life will never be the same again. I know mine wasn't, thanks be to God!
I love you my brother. Be Blessed in the Lord.