Won't crank over?
I'll go with the most likely first:
If it will jump and start...
Dirty/corroded battery terminals. This is very common. The battery will not charge effectively with dirty/corroded connections. The battery will drain.
Loose battery cables.
Dead Battery. Usually without major warning.
Alternator belt loose. Tighten.
Alternator defective. You can replace the diode packs in a 88 chevy yourself.
If it will not jump start...
Battery cables corroded or broken.
Not much left to check.