What does the Bible say about how a sinner comes to Christ?

According to Mark 1:40-42, a sinner approaches Christ just as they are, recognizing their sinfulness without any merit of their own. Coming to Christ involves understanding who He is, worshipping Him as Lord, and pleading for His mercy and ability to cleanse. The leper in this passage exemplifies this by coming full of leprosy and beseeching Jesus, 'If thou wilt, thou canst make me clean.' This reflects the understanding that only Jesus has the power to save and clean them from sin. As John 6:37 indicates, those who come to Christ will not be cast out but welcomed into His grace.