Wowpedia has a page about the Auction House with a section dedicated to describing its UI.
If you know the name of what you wish to find, simply enter all or part of it in the Name field, and click the Search button on the upper right, and the UI will return all the items that match the string you entered. Otherwise, you can search by category: on the left, there are some blue buttons that are preset to search specific categories of items. Click on the category of item you wish the find (i.e., weapon, armor, spell, recipe, etc.). Some category items will then display sub-categories. After choosing the category and sub-category, if applicable, click Search. A listing of the items you requested, if there are any available in that category, will be displayed in the right pane of the dialog.
Many World of Warcraft players who engage in auction more frequently use the Auctioneer addon, which is kind of a "power user" extension to the auction house UI, allowing you to automatically place items for auction and track market trends and prices. It's worth looking into if you want to know how advanced players are interacting with the economy of a major MMO.
Blizzard announced this week that its upcoming non-MMO title Diablo 3 would include an auction house very similar to WoW, but that it would allow players to trade items for real money. It might be worth looking into the UI they're using there to see if there are any significant differences. Gameloft's iOS MMO, Order & Chaos Online, also does this but there's significantly less documentation available - it might be worth it to get it and try it out to see if they differed significantly from WoW's model (given that O&C copies most of WoW's UI in detail), and, of course, since they've created the first high budget iOS MMO and will therefore have had to adapt many principles to a touch-based UI.
I could tell you more about WoW's UI specifically but I think you should ask a separate question for that.