Soak a nonabrasive, lint-free cloth in warm water and add a mild soap. Use your cloth to wipe the underside of the CD in straight movements from the center of the disc outward. Do not ever use a circular motion when cleaning your disc, as this can scratch the surface. After wiping the disc, use a second cloth to dry. Insert the CD into any CD player and see if your damaged track plays.
Squeeze a small amount of toothpaste (approximately half the amount you would apply to a toothbrush) onto a cotton swab and polish the underside of the disc in straight motions to fill in deep scratches. Scratches are often responsible for the skipping in music tracks when cleaning alone fails to solve the problem, but toothpaste can often restore a disc's playability.
Purchase a commercial CD cleaning kit. These kits contain liquid solutions, microfiber cloths and disc-cleaning hardware specially designed for CD surfaces. When home solutions fail, a CD cleaning kit can restore functionality beneath the surface. Follow the manufacturer's instructions for use.
Make a copy of your CD or individual music track using your computer. Insert the disc into your CD-ROM drive and rip the track(s) using your favorite digital audio software, such as iTunes, Windows Media Player or Nero. Remove the CD, insert a blank CD-R or CD-RW and burn the song(s) onto the new disc. Because the ripping process uses a different disc-reading process than a standard CD playback device, you can often copy music flawlessly even when it refuses to play.