Unfortunately the Auction Houses are only accessible from the menus, not anywhere in the game via your character.
The Auction House is a new trading system introduced in Diablo III which shares many features with similar systems found in other games, such as World of Warcraft. Accessed through Battle.net and not from in-game, the auction house allows all players within a region (US, EU etc.) to buy and sell items easily and conveniently between each other. Almost all items other than quest items can be sold between players, and everything is run by the players: Blizzard will not sell any items.
http://www.diablowiki.com/Auction_House
Edit: Blizzard has since confirmed that this is a deliberate design decision (Source).
Contrary to MMOs like World of Warcraft Diablo III is not a game where the auction house meta-game is part of the in-game story.
Determining the "fair market value" of an item is a chore at this point, although I'm certain that at some point in the near future auction house analysis tools will be created by Blizzard or the community.
Market value is likely to fluctuate considerably as people play the game in different patterns, so saying "X is a good rule of thumb," especially in the early going, is a losing proposition. Right now, for instance, low level crafting components are probably vastly undervalued as many people are playing low level areas. When the game starts to age, we'll likely see far fewer low level items, and more bits of high-level components.
Essentially the three pieces of information you're seeing are:
- The current lowest price available for you to buy the quantity of the item in question.
- The average sales price of the last 10 of those commodity sold, which is supposed to indicate the short-term trading value of the item. However, this is unclear as to whether the price is inclusive of "bulk orders" or not - if someone buys 100, what 10 of these count?
- The average sales price of the last 24 hours worth of sales, which is supposed to indicate the long-term trading value of the item. However, this appears buggy - at times, this has read 0 for extended periods, even though it's clear there are many sales going on.
If you're listing a commodity below the lowest price on offer, and then not seeing the buyout price change, that's because you can't buy your own auction - so you're seeing the next cheapest item for sale from another vendor. This is what you'd want if you're going for a quick sale, but might not be what you want if you're trying to maximize profit.
As far as pricing your own commodity auctions, I've found that only empirical data sampled over time is available at this time. For instance, I'm often buying Square Rubies, and I know that around ~8k gold is an "average" price - I see them listed for far less and occasionally try to buy, but frequently am out-sniped. If all I see is 10k+ gems on offer, I'll probably wait for a price break.
Selling is similar to buying, just in reverse. If you've got something you think is particularly valuable, sample the current values of the 3 pieces of information you have available, and then watch for times when the current market price is above what you've determined is fair. Then you can list your item slightly below this and turn a profit, or list it at what's typically "average" for a quick sale.
Best Answer
As Blizzard take a cut of your final sell price, they won't have an issue with you advertising the item both in game and outside of the game. In fact - they even provide a trading forum on the official Diablo 3 forums (EU, US) and a trade channel within the game itself.
The only thing that I could see you doing while advertising that might cause issues is if you ultimately end up spamming trade too frequently to get yourself seen, or bumping your forum post on the official forums too frequently. Blizzard's general rule on this is not to bump any thread of this nature until it falls off the first page.
Any actions that you take on third party forums are not bound by Blizzard's rules.