It's easy. All you need is:

Put one or two drops of scratch remover on the cloth. Rub gently the affected CD surface, from the center to the border and back. Always rub this way, never sideways or in a circular motion.

That's it! This will remove light scratches completely and clean the big ones enough so your CD player can see through without distortion.

If you don't feel confident about this procedure, just get one of those useless AOL CDs, scratch it, and use as your test subject.