It's either loose or you have a bearing going out on idler or an accessory.
That depends on how, when and where it is squealing. For example, if the brakes squeal when applied, the brake pads are probably worn down. A squeal from the engine compartment whenever the engine is running could be a loose serpentine belt (especially if the squeal changes a little when you rev the engine).
Maybe the tires? If it is in the engine compartment, it is probably either a loose belt or one is getting old and slipping.
The belt could be damp, loose or slipping.
A loose belt. Most likely the alternator belt, if it doesn't squeal when you make a sharp turn.
either the belt is worn to the point of breaking or its very loose
Belt may be loose or glazed
Normally this is caused by a drive belt that is loose or worn and needs replacing.
The squeal when you turn on the AC or heater is a loose fan belt. It may be cracked and need replaced, or it may just need tightened.
Most likely it is a loose fan belt (commonly used on older vehicles, prior to the newer serpentine style belt). The fan belt can be tightened by loosening the alternator mounting bolts and adjusting the alternator tension on the belt.
A loose, cracked or dry belt.
Very often it is not the alternator, but the belt that squeals. This can be checked by rubbing a little soap on the belt, if the squeal goes away, you know it's the belt. The belt may squeal for a number of reasons: the belt is new, the belt is old, the belt tension is too tight or loose, the belt is cold (the squeal goes away on it's own when it warms up). Some belts just squeal for no discernable reason, but there are 'belt dressing' sprays available for sale that sometimes help. Always check the belt before spending a bunch of money on a new alternator that may not be needed.