Buying a used car is a bit trickier than buying a new car although you can follow most of the same guidelines for both.
First, know what car you have in mind. Research the car. There is a wealth of information online. Check the car manufacturers web site, consumer reports and the edmunds.com. web site. Know the approximate value of the car before you head out to the dealer. Go to your bank or to your credit union before you go shopping and see how much money they'll be able to lend you on a used car. This way you'll have a much better idea what you can realistically spend.
Realize that there are many different models of the same car. You may not find exactly the car with all the extras you want, or the exact color, but you may find something close that is a great deal.
Most dealers are upright and honest when selling used cars. They offer limited warranties with them. In the case of luxury end cars a lot of them still have warranties in effect when you purchase them.
If you are buying from a private seller ask to see service records. Go online and order a carfax car history report. Find out if the car will be sold "as is" or already state inspected. When you are serious about a used car make sure that you have time to take the car to your mechanic for him to give the car the once over, especially if it's being sold "as is". You don't need to find out after the fact that it needs many more repairs than you thought. You can't tell just by a visual inspection.
The cosmetics of the car are an important factor in determining it's value. Cars are generally rated as being in good, fair or excellent condition. However, especially when purchasing from a private seller you'll find that these ratings vary, sometimes greatly.
Whatever you do, don't let anyone pressure you into making a quick decision, especially a private seller. If you hear something like "I already have someone else who's willing to give me a down payment" let the car go. Stick to your guns, and your budget. If you don't get this car it wasn't meant to be and there will always be another, and better one.