What type of guns are you looking at?
Different kinds have their own little peculiarities to check for.
Overall condition is the first thing to look at, wood/metal finish consistency is important, if finish doesn't match something might have been replaced.
Not necessarily bad, but could be a sign of an underlying problem.
More important to me anyway, is a basic function check.
Work the action, make sure the safety functions, drop the hammer, (ask first) look for unusual roughness or tight spots in operation.
Unusually loose parts, faint cracks in wood or very rarely metal(!) in high stress areas, and of course evaluating bore condition is its own science.
Check the crown of the barrel for sharp lands and grooves, then shine a light through the bore and check for spots of rust and overall condition of the rifling.
A little dust is fine, but if you have any doubts, ask to run a patch through the bore.
Check the chamber for rust, a pitted chamber can be very problematic in a rifle, handgun, or shotgun.
These are some very basic tests, not in any particular order. Lots more tips I didn't mention.
Cheers!