I would start by confirming the battery has 12.5+ volts. If it clicks and has 12 volts it is likely the starter or its power connections. If it doesn't then you need to start looking at grounds, the main power lead to the starter, posts on the battery, and signal to the solenoid.

Not to be flippant but this is something you can google a guide for. This is not going to be vastly different between a R107 and a 90's GM.