Keeping in mind that CD's should be cleaned as little as possible, if you'd like remove smudges, apply a little rubbing alcohol to a clean white cotton cloth and wipe it ACROSS the CD. Never use a circular motion when rubbing, as this will create scratches.
In order to fix CD scratches you can also get a little clothes washing detergent and dilute it in water. Then take this and put it on a rag or paper towel. Wipe the CD from the center to the edge of the CD. P.S. This will also fix DVD's.