An illuminated alternator warning light typically indicates a low electrical charge. An automobile may run for an hour or so with a failed alternator, but the car needs to be driven to a safe location as it is unlikely to restart.
Problems with the alternator drive belt will cause the alternator to not properly charge the electrical system. A worn belt may stretch or otherwise fail to grip the alternator pulley. Worn drive belts will show cracks, hard spots or have a glazed appearance, all of which will require the belt to be replaced.
Loose or corroded wiring can cause the alternator charge delivered to the engine to be low. Alternator wiring should be checked to ensure that lock nuts are tight, and that the connections and wiring have not been damaged. Battery terminals and cables are prone to corrosion and should be inspected as well.
A bad alternator will often begin to make grinding noises as the internal bearings wear. However, an alternator may also fail without creating noise. A voltmeter can be used to test the voltage output of the alternator, but auto parts stores will typically test alternators without charge.