First off, let me say it. Yep, it's SNOWING! Welcome to Colorado lol.
Auctions can come about in a few different ways--
1. If you're an agent with nerves of steel, a project could come right out of the gate to a few editors in an auction. Basically, you'd be setting up an auction before the editors have even had the chance to read the work.
Now, I could see this working okay with certain non-fiction projects, especially if it was a timely work by a very prominent figure and only if I knew the editors well enough.
2. Your project has been submitted out. Let's say one house comes back with a small offer. My first step would be to call any other editors looking at it and fish for more offers. If we end up with 2 or more offers, then we would consider taking it to auction.
3. Your project has been submitted out (deja vu). We receive 2 offers from 2 different houses at the same time.
So, we've received a couple offers on your work and have decided to take it to auction, then what? Well, first we have to set up the terms of the auction. Not having good, specific terms to an auction can be the ruin of what might have been a great deal.
1- The floor. Every auction needs a number to start. This could be the lowest (or the highest) offer we've received so far, or an even higher number that's been decided upon.
2- How long? You can set up an auction with only 1 round. You give the houses a date to have an offer in, then take the one with the best offer.
Or, you can set up an auction in a few rounds, taking the highest offer from Round 1 and using it as the floor for Round 2, and so on.
Or, you could do a round robin, with rounds going on and on until only one house is left.
One thing to keep in mind is an auction doesn't always go the highest bidder. Sometimes other aspects of the deal (royalty percentages is a good example) more than make up for taking a smaller advance.
Also, many auctions are pre-empted. This is when one house gives a limited-time offer (usually expires in 24-48 hours). This amount generally works in favor of both writer and publisher--more than your agent expected at auction and less than the publisher might have been willing to pay.