What does it mean to believe on the Lord Jesus Christ?  

• You know you know you are a sinner. 
• You believe Christ died for sinners. 
• You cast yourself completely and exclusively upon Him, believing that having this kind of faith is the only way to receive pardon and peace, abandoning all self righteousness and self-confidence.  
• You give up your natural hostility toward God, as well as your rebellion against God, and instead adopt a spirit of grateful submission to the will of Christ through the renewing of one's heart by the Holy Spirit.

How do I go about believing on Christ and repenting,
since I have no natural ability to do these things?

• Look to Christ, speak to Christ, and cry to Christ, just as your are.
• Confess your sin, lack of remorse, and unbelief, and cast yourself on His mercy!
• Ask Him to give you a new heart, resulting in true repentance and firm faith.
• Ask Him to take away your evil heart of unbelief and to write His law within you, that you may never stray from Him in the future.
• Turn to Him and believe Him as best as you can, and pray for grace to turn and believe Him more thoroughly.
• Use the means of grace expectantly, looking to Christ to draw near to you as you seek to
  draw near to HIm.
• Watch, pray, read and hear God's Word.
• Worship and commune with God's people.
• Continue to do these things until you know in yourself beyond doubt that you are indeed a changed being, a repentant believer, and that the new heart which you desired has been put within you.
  
  

  The emphasis in this advice is on the need to call upon Christ directly, as the first step.
  

• The only readiness God requires is that you realize your need for Christ.

• Do not let your conscience delay you.

• Do not delay until such a time that you imagine you will feel ready.