Narrow down the make(s) and model(s) that you are interested in purchasing. Decide if you want something that has already been restored, or something you can work on restoring yourself. Obviously, a restored car will be more expensive than one that needs work, but if you don't have the skills to restore a car yourself, in the long run it is cheaper to purchase a car that has already been restored by someone else.
Conduct research by reading books and magazines about your car of choice. Talk to other people who own the type of vehicle you're looking to buy. Join a car club specific to your kind of car, but also join a local club. Members are knowledgeable about their cars and will have specific information about the kind of car you want. Visit car club websites and forums (such as 442.com or stovebolt.com) to ask questions of other owners. These online networks are also valuable after you purchase your car.
Check for availability of parts for your car. Are they easy to find? Are they expensive? It will be easier to find parts for cars that are more popular, while obscure makes and models will be more difficult.
Compare prices from many sources, including local classifieds, eBay, Hemmings Motor News, and any publications specific to your type of car (i.e., Oldsmobile Club of America, the Antique Car Club of America, etc.). Know how much that kind of car should sell for, so you can negotiate the price accordingly when it's time to buy.
Let folks in your local club know what you're looking for. Car people love to talk to each other! Use that network to your advantage.
Look at many different examples of your make and model before you purchase one. Don't buy the first one you see! You want to make sure you look at a wide variety to find a car that fits your particular needs. Take your time and make the right decision.