1984 Chevy Truck

The simplest way to check the alternator is this --
With the engine off turn the head lights on. Observe how bright they are. Now start the engine. If the head lights get noticably brighter then your alternator is usually ok. Do this at night it's easier to see a change in brightness.
Disconnecting the battery will kill the engine. The alternator charges the battery or keeps a charge in the battery. The battery sends voltage to the ignition and other parts.
Autozone or a place like that will test your battery and alternator for free. This is the best way to diagnosis a bad alternator.