Clean excess mildew off the CD with a soft wet cleaning cloth. Wipe in straight lines from the center of the CD to the edge. Never follow the ridges when cleaning a CD, as that will only spread the dirt around. It could also scratch the CD.
Rinse the CD under lukewarm water and let it dry.
Repeat the cleaning step if mildew is still clumped on the surface, adding a bit of dish soap to the water. Rinse well and dry the CD.
Moisten a soft cleaning cloth with rubbing alcohol. Work your way around the CD, wiping from the center to the edge, until the entire CD has been covered.
Allow the rubbing alcohol to air dry, to give it time to kill the mildew. Rinsing the alcohol off could stop the process.