Look around the seems of the car. The seems should be of equal distance.
The back of the car usually has logos and car model. If anything is missing or doesn't feel right, the body might have been painted.
Check the roof of the car, if it dented or damaged it might indicate a car that's been in an accident.
Check the tire threads, brake pads, and brake discs. If they need replacing you can discuss with the owner and explain that it would require further money. I managed to knock off £150.
If you can check the underbody of the car then do so. You are looking for anything extra shiny or clean. Parts might have been replaced.
If the car has a timing belt then ask when it was last changed. This is important and needs to be changed. It can take a few days to change and can cost a lot.
Drive the car around. What you are looking for our weird ticking sounds or jerks. Also, keep an eye on sudden jumps when changing gears if it's automatic. This indicates an old gear box or some slipping that happens.
Open the engine bay and try and look for any oil leaks. Any leak around the engine gasket is a concern.
Sorry for the long message. Any questions, let me know.