The current Auction House was implemented 15th January 2013. Before it there was a slightly different system in place.
There are 5 different categories in the Auction House; Extremely Rare (249 or less in circulation), Extraordinary (250-499 in circulation), Rare (500-999 in circulation), Limited (1000-2499 in circulation) and Uncommon (2500-12500 in circulation). To check if your item qualifies for one of these categories; hover over an item and click on eye symbol that appears (if you are looking on the Item Market) or click on the item (if it is in your Inventory), from there find where it states "Circulation" and then hover over the symbol that appears next to the amount of that item in circulation. Only these items can be added to the auction house, however they will stay in the same auction category if they go over a limit once already added. You choose a number of days between 3-30 for your item to go on the market.
All auctions start at $1 and there is no reserve or starting price system. The game will automatically bid for you up until the maximum price you have set when you bid. This is to prevent bid sniping right at the end of the auction time. There is a live timer counting down to the end of each bid on the page, which can end at any time of the day. If you are outbid or your item sells, your money is returned in the form of a cashiers check. These can be redeemed at the city bank, or are returned automatically after 24 hours. After the item sells you get given 97% of what the final bid on the item was - with the other 3% being charged as Auction House fees.