Do you plan on buying from a dealer or a private owner? Personally, I would never buy from a dealer, but they're a great place to look after hours if you want to see what's available. You'll also get a good idea of the range of quality (visually). These are probably general guidelines:
Decide on some general feature you want and don't stray from them. Stick or auto? Covertible or coupe? Decide on which model years you're interested in, and a max price. Don't go over your max price. Once you have these general items down, STICK BY THEM! If you're not completely unreasonable in your expectations, there's a car out there that fits your bill.
When I bought my '86 in '92, the ones I was looking at seemed to range around 14-15K, and I didn't think they were in the best of shape. One of the nicest ones I found (it was VERY nice) was the same price, but an auto without the Z51 handling package, which I wanted. It was tough to pass it by since I had been looking for so long, but the very next day I found the exact car I wanted at an excellent price. The guy had it listed for $12k that day (sunday morning), and I offer $11500. He probably would have taken 11k, but I figured I was getting a steal as it was. He was happy, I was happy. Turned out to be a nice guy who just happened to have 1 too many cars (just bought a mercedes if I remember correctly).
Don't take any BS from anybody, although it's tough to do for the first Vette because you really don't know that much about them. The first one I bought I probably got suckered, but the 2nd one I knew enough about them to take 3 months until I found the right seller.
Take a log book with you when you check them out to write down any details (good or bad) vs. price. You'll soon get an idea of what to look for.
Check for oil leaks, bad smells, and strange noises. Whether or not you can detect such things is going to depend on your knowledge of cars in general. I personally look at the physical shape of the interior as a good indication of how someone would take care of their car overall.