First, read Psalm 51. Also, pay special attention to the title of this Psalm. The story that leads up to the writing of this particular psalm (2 Samuel 12:1-12) is crucial to understanding the intensity with which this psalm is written.
Next read Hebrews 10 and then consider this question. How has Psalm 51:7-12 been fulfilled through the cross? What sort of confidence, then does that give us in coming before God to ask for forgiveness for even our most egregious of sins.
Finally, look closely at Psalm 51:17. Does this verse accurately describe the state of your heart before God?