The tried-and-true cleaning solution is isopropyl alcohol (also known as rubbing alcohol). While some use ammonia-based products (at the risk of warping their discs) and others rely on natural soaps, rubbing alcohol is the smart way to go. Dab a little on an old cotton T-shirt or a cotton ball.
Just like with eyeglasses, the fibers of paper towels, certain sweaters and denim can scratch you discs even worse. Only use soft materials like a cotton T-shirt when rubbing down a disc. Remember, when cleaning a compact disc, you should always wipe in a straight line from the center to the edge and never in circles.
Chances are there's still a used CD or video game store near your home. Find one and bring your scratched discs there. Because they sell used items, part of their process is to clean discs that are sold to them smudged or scratched. They use specially purchased machines and cleaning solutions to repair discs. Sometimes these vendors charge for this service, but if you're lucky you may find someone willing to do you a favor.
You'll find tips all over the Internet suggesting you try using a banana or toothpaste or even peanut butter to fill in scratches. These extreme and strange measures may seem to work, but these food particles aren't going to stay on that disc for long (especially as it heats up and spins in your CD drive. Ultimately, you're going to end up with banana bits in your laptop or chunks of peanut butter in your disc player.