one engine that goes vroom vroom.
Two wheels
one seat

Joking aside, look for leaks after it has been idling for a while. Check the engine is cold then get the seller to start. Pay attention to what he/she does, do they immediately show you it revs through the range (this would tell me they rag their bike as they are not letting it warm up) Does the rear tyre has chicken strips. this give you a good indication how it has been ridden. General condition, smoke from exhaust, etc. rips oin seat, milage, etc, etc etc.

Start from the front wheel and work your way around bit by bit checking everything including chain tension and the other stuff you might not know. Check its clean but not too clean, etcetcetc.

Good luck and enjoy the experience