The primary source of squeal noise in disc brakes is a high frequency vibration of the brake pad when brakes are applied. This is commonly caused by dirt or rust on the back of the pad, and can sometimes be cured (temporarily) by sanding the back of the brake pad to be clean. This may or may not work, and it may not last long. Some mass production fixes may involve a shim between the pad and piston, possibly spring steel or some fiber material, and/or a spring clip on one end of the pad. A generic aftermarket product offers aluminum foil laminated over thin dense card stock, possibly with adhesive on one side.

My favorite cure is a product called "Disc Brake Quiet" from CRC. This is similar to high temperature RTV. Smear a little of this stuff on the back of the brake pad where it will contact the edge of the piston, and any squeal will magically vanish. A 4-ounce bottle for about $5 may be a lifetime supply for most do-it-youself folks. Another similar product is Disc Brake Silencer by Pro Seal (could be the same producer for all I know).