I'm not mechanically minded so I normally take a proposed car on a test drive.
Try and go on a variety of road types so you see how the car handles. Keep the stereo off and listen for any strange noises.
If you can....I'd try to go to an industrial estate/zone to do an emergeny stop to see if anything buckles/if performs how it should. I try to get on a road with no camber and slowly drive 'hands free' to see if the car pulls in one direction.
Don't be scared to push it on a test drive, it's not your car....but it might be. Do some footdown action to see if the cars smooth or not.
Other than that, I usually check all the panels for dings/dents etc and check all the functions work, Roof/Windows/Air con etc..
Not much use on the engine bit i'm affraid...I usually have a quick look and go....ooOoOO that looks nice. Just check everything looks clean I suppose.
Not sure if your buying trade or private but if private i'd defo check the cars history. There are a variety of websites that offer this service now at a reasonable price. Will draw attention to any accidents, irregularities or HPI agreements.
Thanks for that, I'm having a HPI check and have found a website that when you register it tells you what to look for fault wise on any make of car, but they haven't supplied me with a password yet to view !!!