From PsyHelp

The System

Added in mid-January of 2005, the Auction House is a place where residents can sell their rare or otherwise fantastic items to the highest bidder. In an attempt to mimic real auctions, and give people in all time zones a fair chance to bid, the time remaining on an auction is reset to 8 hours whenever someone bids on that item. Once a bid has remained unchanged for 8 hours, the auction ends. The high bidder may claim the item by clicking "see details" then "claim item" or the resident hosting the auction can click "claim bid money" on the details page. If an auction runs for 8 hours with no bids, it closes, and the owner of the item may click "reclaim item" on the details page.

Also, whenever a god reaches high into the 'Rapturous' stage, a special item goes on auction, one that is worth quite a lot. See the temple to find out more.

Hosting an auction

On the main Auction House page, click "host new auction." Enter the starting bid, a brief description or promotion if you choose, and then select the item you wish to auction from the list below these fields. As with selling, trading, and event prizes, any item you wish to auction must be in your storage when you start the auction.

What should I auction?

The auction house charges a 6 money fee for auctioning your item, and this is non-refundable. You should only auction items if you are sure you will make a profit, even after deducting this 6 money fee.

The harder to find an item is, the more people will pay for it, so rare items are the best to auction. Don't auction items that are extremely common or worth 0 money (unless they are rare: for example, the Arcade Machine given to donators in April 2005 has a sell back value of 0 money, but there are a limited number in the game). People with extremely talented pets have an advantage here, because their pets can create or bring home items that are only available to them. Unless new hard-to-get items are added to the game, the number of pets with access to these items will gradually increase, resulting in a decrease in their value. My advice is: if your pet brings you rare items, profit from them while you still can -- unless you care more about keeping items as proof of your pets' achievements than about making money :)