I'm just adding my comment to try and balance out how it read so no one would think that saying a sinner's prayer is dangerous. We would all feel better if a person would use their own prayer to speak directly to God...but there are many people who have never prayed, and that don't feel they know what to say. They beg for help to get past the fear. They feel love for Jesus, but don't have the words.
The best example I can think of when we discuss different people coming to the Lord, is the lives of the early Disciples. They were all called by Jesus Himself and they still didn't know who He was or what He was even doing most of the time they were with Him. However, Jesus still taught them, broke bread with them and loved them because He knew that they were each on their own personal journey to discover who Jesus really was and how He would change their lives forever.
Then you have Judas. He was called as well. However, God knew Judas would betray Him.
Things are not much different today. We still have to wait on the Holy Spirit to fill us when the time is right. :)