Auctions are a great place to find hard-to-get items, profession materials, and items needed for quests.
Buyout
As the name suggests, some auctions will allow you to instantly purchase an item instead of bidding on it (just like "Buy It Now" on eBay).
There are pros and cons for both sellers and buyers with this system. For sellers, the pros include setting a reasonable Buyout may entice someone to grab the item before the auction ends. You may be able to get a slightly higher price from those who need an item right away and are willing to pay for the privilege. It is in your best interest to always include a buyout price. The only real con of setting a Buyout price is that you may set it too low and someone will snap it up and possibly turn around and sell it for more.
For buyers, the main benefit is obviously getting the item instantly. You may also run into items that have a lower than average Buyout price. In this case, you may actually be able to make some money off the item yourself by buying it and re-listing it at its "proper" or more competitive price.
Bidding
Bidding works like any auction: you put in the price you are willing to pay, someone else can come along and outbid you. The person with the highest bid at the end of the auction wins the item.
Just because an auction starts low does not mean that it won't skyrocket toward the end. Keep in mind that some sellers intentionally try to create a bidding war. Before you begin bidding, have a final price in mind. No matter how tempting it may be, don't go over that price - you may end up paying more than you wanted or more than the item is worth!
Other
A seller can cancel an auction at any time, although they will lose the initial deposit (and if the item has been bid on, they will also be charged a percentage of the bid).
If you want to buy an item that has been listed with no buyout price, you can try to contact the seller directly and make an offer. You can also try this with costly items (especially a weapon or armor piece with a high deposit cost and relatively low demand). The seller may agree, especially if they're afraid the item won't sell or if they need money right away.
