DO NOT REMOVE THE BATTERY CABLE while the engine is running! If the generator is working, system voltage can go well over 30 volts and destroy the ignition module and the diodes and voltage regulator inside the generator. On newer cars that can destroy the many computers. Removing the cable was a trick done by mechanics many years ago when they didn't understand how these simple systems work.
Instead, use an inexpensive digital voltmeter to measure battery voltage while the engine is running. It must be between 13.75 and 14.75 volts. Since the battery light is on, we know that turn-on circuit is working. That only leaves the generator / voltage regulator or the output wire between the battery and generator as GarethSturman suggested. If that wire is broken, you will find high voltage on the output terminal on the generator. Another test is to measure the voltage on that output terminal when the engine is not running. You must find full battery voltage there.
To check the belt for proper tightness, try to turn the generator's pulley by pushing on the fan with your thumb. If the pulley spins under the belt it is too loose. Uhm, ... It should be obvious, ... Do that while the engine is not running! :)
Tuesday, March 1st, 2011 AT 2:45 PM