Somethings to do when considering purchasing a vehicle

First thing give it a good external look for any signs of accidents, such as dents or slightly different paint colors as there can be hidden damage in the suspension, frame or body. Also check the status of the title (salvaged or not).

Next start the vehicle and listen to how it runs. It should sound smooth with no rattling or ticking or other weird noises. Older cars make a lot of different noises but common sense should tell you when something is wrong. Many newer cars you can barely tell that they are running. Also check to see if the check engine light is on or any other warning lights.

For most cars with automatic transmissions: with the vehicle running, shift through all the gears twice and check transmission fluid with vehicle in neutral (parking brake on). Shut the vehicle off and check the oil.
It is a good idea to check all the lights (head lights, running lights, brake lights, turn signals, hazard lights and reverse lights.) and the horn at this time.

Next give it a test drive. Try to go a few miles on the street, through speed bumps & dips, and on the freeway. Listen for any abnormal sounds when accelerating, shifting, turning, braking, and going over bumps. Also watch the gauges for any warnings and overheating.

When finished with the test drive take a look at the tail pipe before shutting it off there should be no smoke coming out.

These steps and common sense will give you a pretty good indication of the condition of the vehicle.