1. If it is a mortgage foreclosure auction and the final judgement is let's say $100,000 however the lender has set a final reserve price for $85,000 than you only pay $85,100 unless someone bids more than you. Basically the lender sets the final price and who ever is a successful bidder over that price gets the property. Sometimes that price is hidden so no one know for how much the lender will let it go.
Fine print is buyer beware, any other liens like taxes or municipal lien, building or code violations stay with the property and it will be buyers responsibility. You don't have to pay them at closing which is unusually 24 hours after auction but you need to take in account that you have to deal with them at a later time.
2nd and most important fine print: make sure you know which position of the mortgage you are bidding. If it is the 2nd mortgage that is going up for auction than the property will be subject to all prior liens which means that it will be subject to the first one. So if you bid $85,100 and get the property and there is a $125,000 first mortgage than you will eventually have to deal with the money owed on the first mortgage.
Tax deed auctions are slightly different and are a little safer because taxes wipe out all mortgages but you have to deal with building and code violations.
2. Private auctions usually give you about 30 days to close and you can get title insurance. County auctions are 24hr closing so you can't get title insurance and you have to he either a pro or just lucky. That is why they call it buying at the court steps.