If you go to the auctions, have a selection of cars your happy with, watch the first few of the model your after go through (hopefully the ones you interested wont be the first), you will soon see what the dealers are paying.
To get a car you want, just bid $100 more and you should get it, if an obvious non dealer is bidding then maybe best to let it go, i saw another Camry similar to mine that i was also interested in go through for $1000 more simply because 2 people wanted it.
Not dissimilar to trading really
patience and discipline is required, don't get into a bidding war, if my first bid fails and its usually $100 above what i think the dealers are paying i don't bid again.
Also as korrput has posted, your insurance company will want it insured at there market value which will be quite a bit more than you hopefully will have paid and is basically what you would actually have to pay if you bought from a dealer.
Good luck if you do go to one of these auctions.
If you do not want to go to an Auction, some cars are available pre Auction but will be at the upper end of the expected Auction price but still cheaper than buying from a dealer.