You don't have to find a car where the asking price matches your budget. Asking prices can be totally overinflated. About a month ago I saw a '90 Civic Si hatch advertised on autotrader.com for $6000. That car is worth maybe $2000.

Find a car you would like to buy. Plug the stuff into the edmunds.com "true market value" thingie and if it comes out to a price you like, print it out and show it to the owner. Pretty simple.