I think that there are a couple important things to note about used cars. If you are looking for a cheap used car, don't buy from a dealership. (Dealer's prices on old used cars are way too high because they still try to make big profits on cars. Sometimes, they will make twice as much profit as the car is worth!)
Go to your local bank and get a loan there. If you are buying a $1000-$2000 car, a loan at 12% won't hurt you that much over a year or two.
Next, buying a car with a good reliability record is important (i.e. Honda Accord), but probably not as important as finding a car that has been maintained well through it's life. My Dad still drives a 1988 Plymouth Reliant that we bought in 1989 because it has been maintained well. Most people agree that the K cars had their problems, and most people wouldn't recommend them. However, this one has been maintained well and still runs well.
Consider the mileage that you'll be putting on your car before you buy. If you are going to be driving 50-100 miles per day, you'll probably want to spend a little more and get a slightly newer car than if you are driving 5-10 miles per day.
TALK TO YOUR FRIENDS! Chances are, one of your friends knows someone who has a car for sale! Remember, if someone doesn't have to advertise to sell their car, they won't have to raise the price to pay for the advertising. (I know, advertising a car may only cost $20 to run an ad in the paper, but that means $20 less than you have to spend.)