If your fan belt (now called serpentine) breaks, anything running off it will not work ....like a water pump, alternator, AC, ETC... You can buy one at most any auto parts shop...and I highly recommend you have one extra anyhow...because, if on a trip... late at night, most anyone can change one...but they have to have one to replace...and your not going to find one then.
If your car is older, it might still use fan belts. They are replaced by loosening the alternator, pushing it in till the belt can be taken off, then tightened back after the new belt is on.
On newer cars, the (serpentine) belt is held in place by a belt tension-er. You have to take a 3/8 inch drive ratchet to release the tension so you can remove the belt. Install the new belt the same way the old one ran...( their should be a sticker on the support bracket somewhere showing the belt path) You will have to hold the tension-er down (sometimes this can be hard) to slip the new belt over it. Check that you have the belt in place on all pulleys, before you start the engine
Most cars use the 3/8 ratchet, but your car might be different, have someone at the parts store look and see what you need to change the belt, and keep it, and a new belt in your trunk. (some times a piece of thick walled plastic pipe will help to give you some leverage to move and hold the ratchet...you slip it over the handle like a extension)