#1 Correct size: the bike should fit, do not rely on the seller to do this - if in doubt go and visit a local bike shop first, consult a knowledgable friend, or at the very least check a sizing chart (preferably all 3)
#2 Good mechanical condition: how do the gears work, will the bike need an overhaul, do the hubs and crank spin freely, are the rear derailleur pulleys/chain/cassette teeth/crankarm teeth excessively worn, are the tires worn out, are the wheels true, is there any rust on moving parts?
#3 Good aesthetic condition: is the bar tape in good condition, is the paint sctatched excessively, is there evidence of a crash (was the bike repainted/touched up), does the wear and tear correspond with the current owners account of how much the bike was ridden, how does the wear and tear on the RD pulleys and other moving parts reconcile with the condition of the tires and tape, is the seller saying one thing and the bike saying another, etc.?
#4 Fair price: what are other bikes in this range selling for, does the price match the condition. etc.? Both parties want a good deal, sometimes a fair deal is more appropriate.
#5 The most important rule: Caveat emptor... always remember there is another used bike out there with your name on it. If the deal feels remotely shady at any point, feel free to simply walk away.