CDs usually get damaged because of scratches at their plastic surface.
Dirty solution: Wipe the surface of the CD with an oily tissue.
By going in the scratches, the oil will flatten again the CD surface, thus reducing the scattering of the laser beam by the damaged surface. I have tried once with vegetable oil, and I was able to recover a CD with small scratches. Ideally the oil should have the same refractive index as the CD, which is 1.59 for polycarbonate. Also make sure not to put too much oil: The disk spins quite fast, and you don't want to spread oil inside the CD player.
Clean solution: Buy a product to clean the CD.
I have already seen in a specialized shop a cleaning product presented as a bottle with a sponge on the head. The principle is the same as above, except that the liquid to spread is not oil, but some sort of plastic dissolved in a solvent. Once deposited on the CD, it dries. This results in a more permanent solution to your problem.
In any case, the repairs are not perfect, and I strongly suggest you to make a copy of the CD after treatment.