A fan belt that squeaks or squeals is generally caused by a loose belt. As a rubber fan belt ages, it can get worn out and stretch. Over time it gradually loosens its hold on the pulleys and gears underneath the car's hood.
When this happens, the fan belt does not turn as it should, and instead simply rubs against the metal pulleys, causing the squeaky sound. Eliminating the noise is often accomplished by replacing the fan belt. Any competent auto mechanic can replace the belt and find any other problems with the belt and pulley system while at it.