I filter my search for private party sellers. If there's a good deal to be had, it usually is from someone who was offered a low-ball trade in value for their car, and they're looking to sell it for a few bucks more than the dealership offered in trade in. This is usually lower than what the dealer will re-sell it for.

When I find a few likely candidates, I'll try to see if there's a way they'll let me have my mechanic inspect the car. I'm OK with cars, and I'm reasonably comfortable buying one with my own amateur inspection, but I prefer to spend $100 to have my local mechanic get it on a lift and spend 30 minutes looking it over. I'm usually able to get a seller to agree to this if I promise to buy it immediately after the inspection with cash if the inspection comes back clean.