Finding a good used car can really be a hassle and a lot of work. The best way I have found to shop for a good available car is to stat by looking in the paper to see what is available and the price ranges. I have found that usually a private sale is going to be more cost effective than a sale at dealership because you can usually get the car for cheaper.
In general, I have had good luck with dealing with private people because I think most people are basically fairly honest as long as they know they might get caught. When I am looking for a used car I will always ask the seller if I can take it to my mechanic to have it checked out. You can usually have this check done for about $50 and it is well worth it. You definitely do not want to end up with a major engine or transmission repair the first week of having the car.
Where I live there are available car guides that will allow private parties to buy a small ad and have a picture of the auto that is for sale. This is a great resource because it makes it very easy to compare like models and makes to see what the price range is. I would never buy a car over the phone by just a picture but it never hurts to call the people on a car you think is a good deal and see what they have to say. I have been surprised at how much information I can get out of people by asking just a few questions and then being quiet. People do not like silence on the other end of the phone line so if you ask a question and then pause, the other party will become uncomfortable and will start talking to fill the silence. They may tell you all kinds of things about the available car that you would not learn otherwise.
Available car sales are really the way to go if you want a good car for transportation. But it is also a good way to look for a luxury car. Especially in hard economic times like these you can find some really lucrative car deals as people realize they have gotten in over their heads with payments and the like. You can often times pick up a great luxury car by just taking over the payments. As long as the owner is not upside in the loan, that is he or she does not owe more than the car is worth, this can be a great opportunity to get the available car of your dreams.
I would definitely start looking for cars in the paper and in car sales books in order to find a good deal on an available car.