Standard advice on old Shimano shifters is to buy a can of spray WD-40 and squirt it into the shifter body (you'll want to partially squeeze the brake lever to expose the innards). Once you've flushed the internals of the shifter out, spray in some gray lithium grease.

At that age, it's probably a good idea to replace the cables and housings. Lube everything that can be lubed (derailer pivots, brake pivots, etc.). And your brake pads are probably hard, replacement pads will stop much better.