How To Properly...
Chances are you want to clean a cd because it has developed very small scratches that make music on the disc skip or the game/movie you are trying to watch freeze. There are a few different options when it comes to cleaning the disc.
One, you could go to any retail store and pick up a cleaning kit which contains a mostly rubbing alcohol based solution and a buffing cloths. Some of the fancier kits will come with a device with a hand-crank that allows you to spin the disc in the cleaning solution. I have purchased these devices in the past, and while they are effective to some extent, the overall cost didn't seem worth it. I recommend another method involving toothpaste that works just as well and for far less money.
1. The toothpaste seems to act as a really fine-grit rubbing compound. From my experiences, the type of toothpaste did not seem to matter. Simply rub the toothpaste onto the disc with a soft cloth (I use an old sock), and let sit for a few minutes. The toothpaste will begin to develop into a haze on the disc. At this time the disc is ready to be wiped clean.
2. Starting from the middle of the disc, begin buffing from the center of the disc to the outer edges in small, circular motions. Make sure to use a soft, clean, cotton cloth free of debris, or you may worsen the damage to the disc.
3. Place disc in your device and see if you've improved the situation. Note that if the disc is too scratched or the reflective film that actually stores the data is knicked you may not be able to save it no matter what. Good luck!