Small scratches on the playing side of a CD can be removed with a little brass polish on a soft cloth. Through a circular motion over to the scratch 'polish' your scratch away. Afterwards again carefully wipe with a soft, lint-free cloth.
If the CD 's or DVD' s no longer want to play well because there are scratches on there is now a good opportunity to make it playable again: It goes like this in his work: Doing on the scratched CD or DVD a few drops TurtleWax car wax, rub it around with a cotton cloth. Then vigorously a few minutes in the round polish until all scratches are gone.