In my experience (father working for GM and grandfather owning a dealership).
Since you are looking used - if you find a car on a dealer's (auto manufacturer dealer - back by an auto manufacturer GM, Ford, Honda, etc.) lot that you are interested in, check it out with a mechanic that you trust (shouldn't cost more than $150 but worth it for piece of mind). If you are still interested in the car after the inspection return to the dealer and clearly state that you are willing to pay no more than $500 over what they have into the car (trade in cost, taxes, any necessary repairs, etc. - ask to receipts and paper work) more often than not they will sell it to you on the spot, if not I wouldn't be surprised if you get a call from the salesman within the week saying ok. The only exception to the rule are rare or modified vehicles.
Most high volume dealers would rather not hold on to a used vehicle for more than 30-60 day or less if it is a vehicle made by a competitors brand.
Thanks for this. Clearly a different approach than I've tried or heard. I'm not sure I've found a mechanic around here that I trust though! I've been through 4 different mechanics, all of whom have been either unbelievably bad or a total rip-off... The most recently one seems ok. Perhaps I'll try it out.
Typically, I check KBB and deduct from there to find the price I want to pay. Interestingly, I've found trend with dealers around here: add $1,200 on to the KBB price