From the main page, you can brows, bid, check your auctions, or create a new auction. You can also choose either your faction's AH, or the neutral AH to browse.
You can also access the auction house from the item browser in the armory via a new "Find in Auction House" button on the page.
You can search by type of item -- however, the option that only shows items you can use (like recipes or schematics) is not available.
Each category and sub-category on the AH in game is also available on the web interface.
A screenshot of the neutral auction house.
You can sell items from your bags, or from your bank -- all items that you can list are shown on the website.
Once you've chosen an item, you can list it the same way as you do while in game.
A confirmation bar will show up when your auction has been successfully listed.
You can check the items you have listed for auction via the top tab.
You can also bid on items currently in the auction house...
And watch the auctions you've bid on from another tab.