(BTW, all images link to bigger versions)
Try "AI Servo" focus mode.
About a year or two ago, Daniel Young (AWESOME photographer, by the way - check out his book, The Lindy Circle) suggested this to me. I used to use one-shot mode, but AI Servo will try to track the subject. I think it was made with sports photography in mind, and is totally appropriate for dance. Seemed to help a bit, so I usually use this mode for dances and competitions. I'm pretty sure Nikon has an equivalent mode, but someone (Vicky C.) warned me that it really drains the battery.
Hold your camera as steady as possible, and consider getting a monopod.
Low light may force you to use longer exposures so take a moment and think about how you could keep the camera more steady.. Even at 1/125 sec, I like to use a monopod(a.k.a. "the stick"*). Here is one like mine on amazon. It doesn't take up as much space on the floor as a tripod, and still lets me have some flexibility in moving the camera around quickly. I've seen some article on the internet about using a string, a washer, and a bolt(about $2 in parts) to make one. It may help a little bit, so consider trying that if you don't want to buy a monopod.
I find that it helps to relax and exhale slowly and hit the shutter midway through the exhale(I think it was Michelle R. who suggested that to me). I've found this much more effective than tightly gripping the camera and holding my breath. (Don't laugh- you might do this too!)
If there's a wall or post to lean against, use that. But for most dance competitions I've been to, I'm just standing out at the edge of the dance floor, so I know that's not often available.
* Not everyone refers to them as "the stick." That's just what I call mine after mocking the first person (Darren K.) who recommended that I get one.
Don't track the action after you've hit the shutter
If the action is moving across the floor, it is really tempting to try to track it, especially in rapid-fire mode. But I find I never track the action exactly, and now the background is blurry too. Do the best you can and just let the action move across the frame. If it gets too close to the edge, completely reposition the camera and reframe, but try not to just smoothly track the action.
Don't limit your shooting to when the music is playing.
Don't wait till the song starts to pick up your camera. Often, competitors will have fun entrances onto the dance floor(like Celina in the image on the right). Sometimes in a lineup, they start goofing off with each other. These are often some of my favorite shots. At the end of the song, sometimes they will do an extra dip or laugh about something, or someone from the crowd teases them and they react, which also make good shots. So... Keep an eye on them.
Use the time between songs to delete photos
A 32 Gig card will hold about 1200 RAW images with a 5Dm2. (more like 4000 on a 30D) That isn't as much as it sounds like. Space on the card is at a premium. Any chance you get, try to delete the bad ones and delete what you can on-camera. If you used rapid-fire, you can pick out the best one, or at least delete the worst one. But try to glance up now and then to make sure you're not missing anything. Try to do them in order - remember the index of the last one you looked at so you can quickly jump back to it.
Shots seem more dramatic shooting from a low POV, looking up
Crouch down, sit, or lie down on the ground if there's space. The problem though is that if it's an all-skate, you won't be able to see past the first one or two couples - that's what I figured out this year. But if it's a showcase, spotlight, or phrase battle, it may be something to try, space permitting.
Shooting prelims and all-skates
Zoom in close for the first couple songs
Typically, a heat in prelims will have 3 songs with increasing tempo. In an amateur competition, the songs will be slightly slower. More than likely, no one's going up in the air for the first couple songs (and may even be illegal in Amateur Jack&Jill). There's probably going to be a lot of closed position, and not a lot of extensions. In short, there's no reason to go wide. It's a great time to go to 135-200mm and get some closeups. The shots on the right are from Camp Hollywood 2009. Honestly not my best shots, but for me, they were the turning point. I thought there was something compelling about them and I realized you don't always have to see a dancer's feet. The closeups made me feel like I was right in there with them.
Go a little wider for the last song
Then the third song is usually pretty uptempo and people will swing out a little wider and you may get more shots where you want the feet in there. Maybe 50-70mm or so. Go just a little taller than head to toe to give yourself more flexibility later in post processing. Maybe go 50% or so taller if you expect an air step.
Now and then, look up at the whole floor
I often get caught up looking through the eyepiece and experience much of the camp through a narrow lens, waiting for something to happen or framing the shot. Now and then, look up and try to spot what else might be going on. Usually, I know half the competitors on the floor and struggle to get shots of even a third of them in the course of one song (usually more like half a song). Some will be hidden, and I try to keep an eye out to see if they get into an opening. Look around and see who's facing you and where the best shot may be.