Brake squeal is really a high frequency vibration. In disc brakes, it can be caused by vibrations between the pads and rotors, the pads and calipers, or the calipers and their mounts.
Noise may indicate trouble, but the only way to know for sure is to inspect the brakes. If you find nothing amiss (no worn linings, or loose, damaged or missing parts), then you can try any or all of the following measures to deal with the noise problem:
Dampen the pads
Lubricate the calipers
Replace the caliper hardware (slides, pins or bushings)
Replace the pads
Resurface the rotors
One way to quiet noisy pads is to make sure the pads fit tightly in the calipers. If the pads on a single piston caliper have mounting ears or tabs that need to be bent or hammered to hold the pad in position, make sure the pad can't be wiggled by hand. If the pads have clips, shims or anti-rattle springs, make sure the necessary hardware is in place and properly installed. If you see no such items when you inspect the brakes, do not assume that none are needed. The last guy who worked on the brakes may have left them off. It is always a good idea to look up an illustration or parts list for the brake system to make sure all the required parts are there.
If the pads are installed correctly but are still noisy, one of the least expensive and most effective ways to quiet them is to remove the pads and install insulator shims on the backs of the pads. The shims, which are usually self-adhesive, act like little seat cushions to dampen vibrations between the pad and caliper.
Another option is to apply a noise suppressing compound to the backs of the pads. Some compounds harden to a rubber-like consistency to cushion the pads. Another good choice is to apply a moly-based brake lubricant to the backs of the pads. Brake lubricant is long lasting and won't burn or wash off like brake grease can. If applying a lubricant to the backs of the pads, be careful not to get any on the front side of the pads or rotor!
QUIETING THE CALIPERS
The same approach can be used on the calipers. Cleaning and lubricating the caliper mounts can also help dampen vibrations to quiet the brakes. Vibrations here can be caused by worn or loose mounts or mounting hardware.
If the calipers are badly rusted or worn, they may have to be replaced. But in most instances, you can probably clean them up, lubricate the mounting points and return them to service. You may have to replace the caliper slides, pins, clips and/or bushings, though, if there is too much play or looseness between the caliper and knuckle. Be sure to use a high temperature brake grease so the grease stays where it belongs.