This is taken from a book called “Healing Prayer” by Reginald Cherry, M.D. and it is the best, easiest explanation of becoming a Christian that I’ve read:

There are four basic Scripture passages that outline what you need to know to become a part of the family of God.  They are not complicated or hard to understand. Let them be your stepping-stones to a new life.
First, the Bible says, “All have sinned and fall short of the glory of God” (Rom. 3:23 NIV).  Sinfulness is universal, a fundamental part of the human condition. “All” doesn’t leave anybody out. So we must start by knowing where we stand in God’s eyes.
Second, there is a penalty for sin. The Bible says, “The wages of sin is death” (Rom. 6:23 NIV). That’s pretty drastic, isn’t it?  Sin is no laughing matter.  No wonder it casts such a dark shadow on our pathway and hangs such a heavy load on our shoulders.  We are sinners, and the penalty for sin is death. Is there any hope for us? Is there any way of escape?
Third, yes.  Someone else has already paid the penalty for our sin!  The Bible says, “While we were still sinners, Christ died for us” (Rom. 5:8 NIV). Isn’t that amazing?  Why should He love us so? What a tremendous sacrifice Jesus made on our behalf.  What a wonderful gift is ours!
Fourth, we can claim the benefit of Christ’s sacrifice only as we confess that our lives belong to Him – that He is Lord.  We must also believe that He is alive, resurrected from the death He died on the cross for us.  As we do these two things, we are saved.  The Bible says, “That if you confess with your mouth, ‘Jesus is Lord,’ and believe in your heart that God raised him from the dead, you will be saved.  For it is with your heart that you believe and are justified, and it is with your mouth that you confess and are saved” (Rom. 10:9-10 NIV). Also, “If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness” (1 John 1:9 NIV).
That’s it – that’s all you need to know and do to become a born-again Christian.                Born again? Yes, Jesus Himself used that term to describe the new life He gives to those who come to Him.  He told a Pharisee named Nicodemus that no one could see the kingdom of God unless he was born again – “born of water and the Spirit.  Flesh gives birth to flesh, but the Spirit gives birth to spirit” (John 3:5-6 NIV).
When you are born again, you relate to God in a new way.  He is not simply your Creator but your Father, and you are His child. “Yet to all who received him, to those who believed in his name, he gave the right to become children of God – children born not of natural descent, nor of human decision or a husband’s will, but born of God” (John 1:12-13 NIV).  This is a new and very special relationship.
The Bible also says, “Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new” (2 Cor. 5:17 KJV).
Are you ready for a new life? Pray this prayer with me:

Father in heaven, have mercy upon me, a sinner.  I recognize that I have failed to please You with my life and way of living, and that my sins have separated me from You.  I am sorry for my sins and ask Your forgiveness.  Wash me and cleanse me because of the sacrifice of Your Son, Jesus.  Lord Jesus, I accept You as my Savior and invite You to live in my heart and life.  Send Your Holy Spirit to teach me and guide me step-by-step according to the plan You have for my life.  I give myself to You. Help me to live for You and to do Your will in all that I say and do from this day forward.  I love You and thank You for saving me – from my sin and for Your glory. Amen.

If you prayed and meant it, God has heard and answered your prayer.  You are forgiven. Old things are passed away and all things have become new.  You are a new creation, born again into new life in Christ.  Welcome to the family of God!
Now, as a new Christian, you need to grow and become strong in your faith.  The step you have taken is not the end but a glorious new beginning.  The best way to find the daily nurture and care you need is by talking to God in prayer.  Don’t worry about thee’s and thou’s and theology.  Just talk to God like a Father.  Talk to Him daily, hourly, without ceasing.  You are never alone.
Then begin learning about God and His will for you through reading His Word, the Holy Bible.  Yes, you can understand it.  The more you read it, the more meaningful it will become.  I’d suggest starting with the Gospel of John in a modern translation that’s easy to understand.  You’ll also be blessed by the Psalms and Proverbs.  Don’t try to read the whole Bible all at once, just read some every day.  Open your mind and let the Lord speak to you through the Scriptures.
It’s very important for you to make some Christian friends and start associating with other believers who can encourage and assist you in your walk with God.  Find a good church that offers both support and opportunity for Christian service and teaches you the Word of God.
Don’t try to go too fast or get impatient with the progress.  God will make Himself real to you and help you.  Remember, you’ve been born again and are a spiritual infant.  You need time to grow in strength, knowledge, and wisdom.