I used to own a used car lot, so I have a lot of experience in this area. The cheapest way to buy a used car is through an auction. There are various different auctions all around the country. Insurance, Former government vehicles, police impound/towing co. auctions, etc.
You can easily save at least 100% on a vehicle this way. Most do need some work, but if you buy used auto parts from a nearby junk yard and are somewhat handy, you should have no problem. Even if you were to pay someone a reasonable rate to do the repairs for you, you can still save A LOT. It's easier than ever to find mechanic help (Craigslist, Facebook, etc). Don't be afraid to have a used engine or transmission put in a car if you get it for the right price. Just be sure to check on the price of a used part and the cost of labor. It varies drastically. Could be fun for the right person. A nightmare for the wrong person.
I use [Mod Edit: Link removed.] to find my used auto parts. Just be sure to filter the search by zip code.
Also, stay away from foreign cars with expensive parts and repairs. Stick to Ford, GM, Honda, or Toyota.