I have successfully repaired dozens of audio CDs and DVDs using Brasso and then car wax. I just put a newspaper on the table, set the disc on it, and put a few drops of Brasso on the disc. Then I take a cotton ball and start rubbing the disc back and forth from the center to the outside. This often has to be done VERY HARD (like until your thumb hurts) to remove deeper scratches, and sometimes you have to rub across scratches as well. Depending on the severity of the scratches, this takes about 5-10 minutes, and it's important to finish the task by working in straight passes from the center of the disc to the outside (to counter any of the lateral buffing you may have had to do).
After the scratches have been removed, the disc surface won't look too great (i.e. rather milky). The Brasso residue will have dried off and needs to be wiped off with a very clean and soft rag, taking care not to introduce new scratches. I then apply a couple of drops (not more) of liquid car wax onto a new cotton ball and start buffing the disc with a lot of force, working on every part of the disc surface. This needs to be done until the wax has dried completely and the disc starts to look shiny and new. This process also takes me about 5 minutes or so.
Once all that's been done, I simply wipe the residue off the disc with another clean, soft cloth and the discs are like new. Honestly, you can't even tell they've ever been scratched.
