
They discover that the sin in their lives is proving to be a barrier between them and God.
They see that this will result in permanent separation from God and usually, at this point, attempt to remove the sin themselves - which is impossible.
They then discover that there is a way forward and it is one which God has already done for them.
God the Son, Jesus, has died on a cross. He was without any sin and therefore this selfless act can 'buy back' our sin; the sacrifice was big enough to cover all sin for all time. He has taken the merited punishment on our behalf.
All the would-be Christian is required to do is to: admit the sin, repent it, thank Jesus for what He has done and invite Jesus into his/her life.
That person is now a Christian.
Living the Christian life? - Ah, well. That is another story and for another time.