Squealing brakes is a common problem, and there's no one simple solution to it.
It's caused by the friction of the brakes against the rim flexing the brake arms, which then slip back, grab, slip back, grab, etc. This process happens at such high speed that it often causes an audible vibration.
All brakes do this, but with luck the pitch (frequency) is too high for human hearing.
This is generally annoying, but not a safety issue. Unlike automotive brakes, bicycle brakes that squeal are usually in good functional condition.
Here are some things to try if your brakes squeal:
* "Toe in" the brake shoes, so that the front edge of the shoe hits the rim slightly before the rear edge.
* Clean the rims with a good, oil-free solvent (citrus, alcohol, something like that.)
* If the pivots of your brakes are adjustable, make sure that you've eliminated as much play as possible without causing them to bind.
* Different brake shoes may help.