While I'm mostly going to focus on methods and framing here, let's get the must-know technical tricks out of the way first.
Spray and pray
Hit Alt+Z to make your interface disappear. Unless you're purposefully taking pictures of your UI, a gleaming row of hotbars doesn't help your picture look awesome.
Hold down the right mouse button to scroll the camera view without moving your character. This is how you get pictures of the front of your character.
Experiment with your zoom buttons; the mouse scroll wheel zooms by default.
Don't ignore your graphic settings. You can turn them all the way up for an amazingly detailed picture or even turn them down for a clear, instructional screenshot.
While the spray and pray method of photography is muchly maligned by veteran photographers, it's still a valuable aid to anyone working a digital camera. Spray and pray is equally worthwhile to a WoW
enthusiast. Each screenshot takes up a miniscule portion of your hard drive's memory -- why not shoot rapid-fire photos and hope for a bit of luck?
The spray and pray method says that if you take thousands of pictures, chances are, a few of them have to be good. Of course, sorting through those thousands takes a lot of time, and your eye for composition is still the key component in decided which screenshots are the best. But still, you don't lose much by taking a bajillion screenshots and hoping for the best.
Rule of thirds
Without getting deep into photography philosophy, the rule of thirds basically says you want the key element of your picture off-center. It should be about one-third into the photo. (This is a general rule, mileage varies, etc., etc.)
When you're taking profile pictures of your characters, avoid the temptation to frame your character dead center. At best, it'll look like a yearbook picture. Take the time to experiment moving your character off center and putting some fun elements in the rest of the picture.
Taking action photos can be tough. This is why you've practiced the spray and pray method. As soon as something exciting starts happening in-game, mash that screenshot button like your life depends on it. Don't wait for something to happen; you'll have to anticipate it. Start taking screenshots as soon as you pull the mob and don't stop until one of you is dead.
You'll have to go back into the logs and figure out which pictures really worked, but hopefully you'll have a few.
Anticipate those special moments
One of the most important parts of taking in-game screenshots is being prepared. Have a list in your head of special moments you want to capture in pictures. Your first mount, hitting the final levels, or maybe killing the big bosses.
While knowing you want a screenshot won't magically make your pictures better, per se
, it will definitely keep you from looking back and thinking, "Gosh, I wish I'd taken a screenshot."
Visit the WoW Rookie Guide for links to everything you need to get started as a new player, from how to control your character and camera angles when you're just starting out, to learning how to tank, getting up to speed for heroics and even how to win Tol Barad.