Well the prancin pony is always nice but lets try and help the guy here.
I check the barrel rifling with a light, I also check the lock up of the slide and I like to test drop a magazine a couple of times to make sure it ejects, basic functionality, it also kinda depends on the weapon also, 1911 vs glock is a very different check. On a 1911 you would want to test the tightness of the action and dry fire the trigger a couple of times. I am no smith or appraiser but I am very picky about weapons if something seems out of the ordinary I would avoid it.