Ecomike said:
Check the voltage at the battery with the engine running right after starting it, it should be about 14 volts, and later it should read at least 13 to 13.5 volts with the A/C and blower on high, head lights, brake lights....etc all on. If it reads 12.5 volts and drops under 12.5 volts with the head lights on the alternator is dead, or there is a wiring problem.
What year is it?
1990, according to the subject line. That means RENIX with the Delco CS-130 alternator.
Check alternator and battery function as follows:
Using a good voltmeter, connect it across the battery posts. You should read:
12-13VDC with engine OFF.
9.6-10.8VDC with starter CRANKING.
13.0-14.0VDC with engine RUNNING.
Verify engine RUNNING voltage at the post on the back of the alternator, and at the screwpost on the start relay (front of the relay cluster - it should be the only metal box there. The four behind it should be about 1" cubic plastic boxes - and the whole is just aft of the battery.) Reading at the alternator should be withing about .25VDC of the battery (and a bit higher,) and at the screwpost on the start relay should be within .1VDC of the battery (also on the higher side of the battery reading.) This will also serve to check your connections.
If you see nominal output voltage - or higher - at the alternator but not at the start relay screwpost, you've managed to blow out your fusible link (it's between the alternator and the start relay screwpost - which is used as a "distribution post" for your vehicle power.)
It's possible that a battery on its way out could kill your alternator and/or regulator...
Matt Currie is also entirely correct (and beat me to the punch) - the RENIX voltmeter in the IP is a notorious liar, and meant more for "state of charge" indication than as an absolute voltage reading. Suspect IP voltmeter readings should be verified or refuted using a decent DMM.