The most common wrong way to compete
I've said this before, but it bears repeating. If you have to camp the auction house to make a sale, you are doing it wrong. The auction house is designed so that buyers can sort their search results so that the cheapest items appear first. If you are pricing something just barely under what your competitor is posting at, you're asking to be undercut right back. Especially if you're competing in a market where the deposit fees are low and there's a reduced cost to cancel and relist.
This nickel-and-diming may make you feel clever, but don't be fooled. Even if you just sit in the AH watching your auctions, cancel/relisting them when they're undercut, you're making less gold than you would by spending this time doing something more productive. In most markets, most of the time, the most money per hour can be gotten from undercutting by a non-trivial amount. This makes your competitors have to work much harder to re-undercut you.
So what can you do? Aside from pricing your goods to move, there are some other tactics you can use to help your profits and hurt your competitors'. The most effective one is to squeeze their supply. You have two types of competitors: the ones who buy mats and craft, and the ones who farm mats and craft. I'll start with the farmers. How can you compete with free?
Competitors who farm
Farmed mats are not free! The fact that some people think they are just means you have an advantage over them. A typical situation I've seen is where someone farming, say, herbs is selling, say, flasks. You calculate your cost based on the cost (or AH value) of the herbs you use. All of a sudden, someone lists a largish batch at just under your cost. You buy it out, and they relist another batch. At some point, one of you sends a tell to the other, and your competitors smugly informs you that they will always be the lowest price on the AH because "farmed mats are free." Reply with an "OK, you win. /sigh," and keep buying them out.
Farmed mats are worth what they sell for on the AH. The opportunity cost of using the herbs in the above example for flasks is what your esteemed competitor would have made selling the mats instead of the flasks. Of course, if he keeps listing, you'll eventually have more than you could ever sell, right? Wrong. Real players have limits on how much they can grind in a day. Chances are that's much less than you can make from AH purchased mats. Keep buying them out until they run dry, and then maybe send them a thank-you note for having reduced your costs.
Competitors who craft
Much harder to deal with are crafting competitors. These guys have the same sources, resources, addons, information and skills you do. Tightening their supply is an excellent tactic to use, however. Assuming you're not on a realm where it's physically impossible to exhaust the farmers, you can accomplish a lot in a lot of markets by simply figuring out a choke point in the production of whatever market you're fighting over and buy it all out.
Again using my above example: A bunch of flasks take Lichbloom, a moderately rare herb that's used for a lot of things. If you decide to choke your competitors on this, you'll need to buy out all the reasonably priced supply for long enough that they run out of stock and have to buy more at higher prices on the AH.
Now this is actually not the ideal market to get started in with this tactic for a few reasons. Mainly, most serious herb buyers rarely buy off the AH and instead buy directly from the farmers. In this case, your competitor's farmer has to check the AH to see that he's getting fleeced. Additionally, not a lot of people have the cash needed to strangle the supply of as large a market as Lichbloom. Still, if you are feeling adventurous, just make sure you get the stock on both factions or else someone will just make a killing moving stock over to your side.
A much better example of a market like this is the Essence of Fire. It's only farmable in rarely frequented old world instances and is a critical ingredient for some very popular markets, including fiery weapons and Fused Wiring (a component for several markets). All you need to do to knock someone out of the fiery enchant market is to make these cost way too much by buying everything below a threshold.
What's caveat venditor mean?
The universal problem with trying to choke your competitors through their supply is that it encourages people to farm more and raise prices. I used to mine a lot of ore in The Burning Crusade, and nothing made me happier than when someone tried this. In fact, I would make a point of always keeping a bunch of stacks of (at the time) Adamantite Ore in my bank, just in case I'd ever find someone dumb enough to pay four times the market price for them. You can never do this for long, so make it count. Constrain supply for a couple of days before Tuesday's AH rush only if you will make back your investment during the rush.
Being an auctioneer is like being able to print money (or gold, as it were). Wait, that doesn't make sense ... You can print on gold, but you can't print gold. That would be closer to transmutation? I can transmute titanium, but that's only worth it if the price of saronite is low enough to justify the time spent making it. I need some sort of analogy here. ... Whatever, I'll figure it out later. Making gold? Every week, Gold Capped will teach you the tricks of the trade, from setting up your auction addons and user interface, to cross-faction arbitrage, to learning how to use your trade skills.