The auction house is just that: an auction house. A place where you can bid on items, or put up some of your own. A wonderful place to go to look for crafting materials or items. To use it, just walk up and press f. Then using the various menus, select what you want to bid on, or put up for bid.
Buying is just like any normal auction. Put up a bid, or buy it out. Make sure you have enough credits first. Once you are done, to collect your items, go to the Shipping & Reciving Office, located opposite.
Putting your items up for sale is easy, but experience helps to know what price to put them up for.
First off, open up the appropriate menu. Then, choose what time you would like (12, 24, 48 hours), then type in your starting price and buyout price. I recommend putting the buyout price a few hundred credits higher than your starting price: enough to make a profit, but not too much so that no-one will ever do it. Remember, put your starting price to the minimum you want to earn. Some people pay 1 credit more than required, if no-one else bids on it. Then click on your item, and you're away. You can check on or cancel your auctions at anytime by going to the my auctions menu. Oh, and it does cost to start an auction, but a trivial amount to what you can make.
To collect your money or returned items, go to the Shipping & Reciving Office, located opposite.