I've made a ton of gold doing this - thought it was about time I shared some tips and tricks. 
The Basic Idea
Buy cheap armour and weapons, disenchant them, and sell the resulting crystals/shards/essences/dusts for a profit. Easy!
Addons
I use three:
Auctioneer (http://www.auctioneeraddon.com)
Tracks Auction House prices, adds improved searching/sorting capabilities, suggests prices when creating your own auctions, and automates the posting of multiple auctions. This is a must-have addon for anybody using the auction house.
Enchantrix (http://www.auctioneeraddon.com) - included with Auctioneer
Comes with a database of disenchantable items, and what they disenchant to - helps you choose which items to buy. (If you want to sell enchants as well, it will help you calculate what to charge for them based on Auctioneer's prices for the reagents).
(As of this writing, the release versions of Auctioneer and friends are not WoW 2.x compatible, but the Beta version at http://www.auctioneeraddon.com/dl/AuctioneerComplete/ seems to be pretty solid now).
CT_MailMod (http://www.ctmod.net) - part of the CTMod package
Automates the sending/receiving of mail - open up to 50 mails with one click. You will be dealing with a lot of mail if you start doing this seriously.
Preparation
* Use Auctioneer to scan the Auction House. If you haven't used it before you should run scans regularly for a week or so, so that it can build up a good database of prices. Prices vary through the week - usually higher at weekends - and to a lesser extent through the day, so it is important to scan regularly over an extended period. To speed up the scans you can configure Auctioneer to scan only in the Trade Goods category, unless you are interested in prospecting in other areas.
* Train up your enchanting. As of patch 2.x, the maximum level of items you can disenchant depends on your enchanting skill. To disenchant items up to level 60, you need skill 225. You can train up to skill 60 with disenchanting alone which is a start; consult one of the 'powerskilling' guides in this forum for details on how to skill up efficiently from there.
* Learn how disenchanting works. When you disenchant an item, it may disenchant to several types of reagent - perhaps more than one reagent of a given type, but never to more than one type. For example, a level 41 green armour piece may disenchant to 1-2 Dream Dust OR (less frequently) 1-2 Greater Nether Essence OR (even less frequently) a Large Radiant Shard.
Weapons and armour disenchant to different items depending on their level requirement:
Levels 1-10: may disenchant to Strange Dust, Lesser Magic Essence or Small Glimmering Shard
11-15: Strange Dust, Lesser Magic Essence, Greater Magic Essence, Small Glimmering Shard
16-20: Strange Dust, Lesser Astral Essence, Greater Magic Essence, Large Glimmering Shard
21-25: Soul Dust, Greater Astral Essence, Large Glimmering Shard
26-30: Soul Dust, Lesser Mystic Essence, Small Glowing Shard
31-35: Vision Dust, Greater Mystic Essence, Large Glowing Shard
36-40: Vision Dust, Lesser Nether Essence, Small Radiant Shard
41-45: Dream Dust, Greater Nether Essence, Large Radiant Shard
46-50: Dream Dust, Lesser Eternal Essence, Small Brilliant Shard
51-55: Illusion Dust, Greater Eternal Essence, Large Brilliant Shard
56-60: Illusion Dust, Greater Eternal Essence, Large Brilliant Shard
50-60: Nexus Crystal from Epics, and very rarely (<1%) from Rares
Notes:
* Dusts drop most often from armour; essences from weapons. The only exception is Astral Essence, which drops exclusively from level 16-25 armour, never from weapons.
* Dusts and essences drop in larger quantities in higher level brackets (if they appear in more than one), e.g. a level 36 item may drop 3-5 Vision Dust, while a level 35 item may yield only 1-2.
* Blue items (nearly?) always yield a shard; greens yield one 4-5% of the time.
* Some green weapons/armour are not disenchantable at all, so be careful when bidding. Prominent examples are enchanter-crafted wands and the Twilight Trappings items (Twilight Cultist's Cowl etc.).
Buying
With Auctioneer and Enchantrix installed, when you mouse-over an item in the auction house a tooltip pops up telling you what it could disenchant to, with probabilities, and an expected value based on Auctioneer's price database. Because disenchanting is somewhat random, this is only a statistical estimate, but a good guide if you are disenchanting on a large scale. The simple rule is, if the item is 'cheaper enough' than its expected disenchant value, buy it!
You can look for good buys in any way you like, but I generally do the following:
1) Pick a level bracket (say, 46-50), item type (weapon or armour) and quality (uncommon or rare) and Search.
2) Look at a match and note its disenchant value in the tooltip. The value should be the same for all items of the same quality in the search results.
3) Figure out a maximum bid price. I usually bid up to 80-85% of disenchant value, but you may want to be more conservative. Remember that when you sell an item, the auction house takes a cut of 5% of the final sale price, so bidding much above 90% is a bad idea unless you have good reason to believe the estimate is too low.
4) Sort the list by current bid
5) Work through the list bidding on everything until you hit your bid limit. Remember to check all the pages.
Tips:
* If an item has a low buyout, or a buyout very close to its current bid, you may want to buy it outright instead of bidding
* If an item has a very low bid, consider bidding higher than the default to discourage others from outbidding you - better a smaller profit than none at all.
* Supply, demand and prices change, so don't be rigid in choosing your bid limit. If a reagent looks particularly rare at the moment, consider raising your limit. If there's an oversupply of a reagent, or you have a ton of it yourself already, you don't need to be so aggressive.
* Concentrate on level brackets which provide items you need, or think you'll need. Don't bid blindly on everything, or you'll end up with a huge surplus of certain reagents and fill up all your bags.
Disenchanting
Not much to say here. Grab your winnings from the mailbox and disenchant them.
Don't be disheartened if you make a loss on an item. So you paid 2g50 for something that yielded one lousy Illusion Dust; but next time you may get two Greater Eternal Essence from the same item - instant 10g profit. It's a gamble, but if you bid sensibly, the odds are in your favour in the long run.
Selling
It's mostly the same as selling any other type of item - know your market and set your prices accordingly. However, a few tricks:
* Lower level dusts and essence (up to level 40) are mostly bought by people who are skilling up enchanting themselves, and are buying in large quantities. You can save yourself some time by selling only full stacks of these reagents. Lower level shards (glowing and below) tend to be hard to sell - learning enchanters usually go for the dusts and essences because they're cheaper.
* At higher levels, there are still people skilling up, but also non-enchanters buying ingredients for individual enchants. I usually sell singly and in stacks of 5, 10 and 20 to cover all bases.
* Check prices for different quantities individually - single items and small stacks are often more in demand than full stacks, and can be sold for proportionally more.
* Keep your bid price close to or even the same as your buyout, to avoid people bidding, winning, and undercutting you. There is no deposit on enchanting reagent auctions, so no penalty for them expiring. I have mine set at 95% of buyout, but I sometimes go a little lower if I want to undercut someone.
* Watch for disparities in the prices and supply of lesser and greater essences: lesser essences often sell for more than a third of the price of greater ones. (I guess many people don't know that you can split/combine them).
* Don't flood the market. You may have 20 stacks of Vision Dust itching to be sold, but it's very unlikely that you'll get rid of all of it in 24 hours, and oversupply drives prices down. I usually limit myself to 4 stacks of dusts, 2 of essences, and 1 of shards, sometimes more for the lower level reagents that tend to sell in large quantities if they sell at all. You can always replenish your auctions if some of them sell.
* If you find you are running low on a particular reagent, jack your prices while you restock. Far better for your auctions to expire than to run out of a reagent when there's a shortage, and see people selling it for twice its normal price.
* Adjust your prices to track the market, but don't lower them too far. Floods never last forever, and after a while you should get a feeling for a baseline price where things will always sell eventually. Enchantrix includes some built-in baseline prices, used in the tooltip, but they may not match your server's economy; you can adjust them by editing the .lua files if you like.
* Use Auctioneer's 'Post Auctions' pane rather than the default UI. If you have scanned recently (always a good idea before posting auctions) it displays a list of other auctions for the same item to help you choose a price (or buyout cheap auctions). It can also automate the posting of multiple auctions - e.g. 10 auctions of Illusion Dust@1g20.
* In recent versions of Auctioneer, manually searching for an item using the regular 'Browse' UI - and viewing every page of matches - updates Auctioneer's prices for that item, so you don't need to do a full scan if you are only posting a few different types of item.
And that's it