Before I abandoned my mighty mouse for a magic mouse this is how I cleaned the ball when it would stop working:
1. Wash your hands so that they have nothing on them to contaminate the mouse further.
2. Take a Q-tip (aka cotton swab), and dip it in some rubbing alcohol, roll the moistened tip on a towel to remove the excess.
3. Run the Q-tip over the ball in all directions, occasionally stopping the ball from rolling with a fingernail. Do this until you no longer see any evidence of dirt/lint coming from the ball. You might have to use the other end of the Q-tip, and redo step 2, to continue cleaning the ball if the first end becomes overly dirty.
The most important thing to keep in mind is that anything you have on your mouse hand is going to gum up the ball, so make sure that hand is clean. No eating chips, etc with that hand.