I would suggest looking for a used car in the Auto Trader (Thats what they are called here) magazines you usually see by the exits of gas stations (and it should be free). Anyways look around and if you see something you like, call the person who is selling it and arrange to look at the car.
Visually inspect the car. Try to avoid anything that has been wrecked and fixed, because that will often cause troubles down the road.
Check the engine. Make sure it is in proper shape . Make sure to check the fluid levels and the tires, since that will give you an idea on how well the previous owner treated the vehicle.
Millage is a big factor to consider when buying a car. For older cars be weary of any around 100K. With newer cars (90's), however have been known to go well past 100K if properly maintained.
Test drive the car with the radio off and the windows cracked so you can listen to the motor. While driving check to make sure everything works as well and see what sensor lights are lit on the instrument panel.
Ask the previous owner about the car (but take everything they say with a grain of salt, since they are trying to make money off of you).
If you are satisfied with what you find, get a Carfax report. Even if you are confident with the car you find, you never know what kind of troubles that car has faced in the past, and there could be alot the owner did not tell you about.
Also this page will help you determine a cars value so you don't over pay.
http://www.kbb.com/kbb/default.aspx?trid=20&psid=1-114-6429-5-1-3&gclid=CKTRvo7Ll5ACFQGRPAodCnnR8Q