Dance photography is the art and science of taking, processing, and printing pictures of people. Who are dancing. That's the quick version.
The long version is that dance photography takes a particular natural talent, vision, and the usual practice. For the love of god, practice. I'm also assuming you already know the fundamentals of black and white photography pretty well. With that said, here are ten tips in whatever order I feel like putting them in.
1. Practice. You won't get better without it, I assure you. And it's fun! ...Right?
2. You have to enjoy taking/processing/printing photographs or those long hours in the darkroom will feel less and less like an entertaining escape from reality and more like another day at the salt mines. You don't need another miserable time-consuming experience in your life, do you? (and if you do, come do my laundry.) Enjoy yourself. Listen to music. Introduce hot friends of the appropriate sex to photography, then encourage them to work with you. It might work or it might not, but it'll probably be more effective than teaching them to play Nethack.
3. Dancers are either prima donnas or genuinely nice people. That's a good thing. It means they'll be your bitches for a while if you ever feel like shooting a few rolls without the stress of shooting during some company's dress rehearsal (or, god forbid, performance.) What I've done in the past when I was experimenting with infrared film for the first time was have the dancers run through their routines, then improvise some poses in front of a mirror. If there's more than one (two in my case) or if they're experienced dancers they can usually think of something. I was shooting infrared slide film which requires considerable bracketing, so the six poses they could easily think of were plenty. And don't make them stand in uncomfortable positions unnecessarily. They really hate that.
4. Overexpose your film. If you try to overexpose your film while taking dance photos under typical stage lighting, one of two things will happen: You'll either get the correct exposure, or you'll underexpose the film despite yourself. Actually, taking photographs that come out well under stage lights is usually pretty easy if there's a black background. Black stage curtains are a great background because you can leave them in if they look good, or you can expose your print until they become solid black.
5. Choose your locations. Isolating and emphasizing the dancers (which is probably what you want to be doing, since it is after all dance photography) is much easier with one of my two favorite setups: The empty black-box theater surrounded by black curtains, and the dance practice room with a giant mirror for one wall with the other walls covered by black curtain. The only things in these environment that aren't black or very dark gray are the dancer, the lights, and YOU. I mention you because if you stand right in front of a dancer with a mirror behind you, you'll show up in the mirror (and consequently the picture). Oops. It can be hard to get the perspectives where you want them without showing up in the picture yourself, but try. Nothing is more painful than having a great picture ruined by your elbow sticking where it can't be cropped. Except possibly unrequited love.
6. Shoot piles of film. If you're not sure whether or not to take the shot, take the shot. It might cost a little more, but you can always decide it sucks on your contact sheet.
7. Make contact sheets.
8. Organize your contact sheets. A three-ring binder works pretty well, along with stapling your contact sheets to the corresponding negative carrier. Note I'm using the 'polyethylene sheet you slide your negatives into for safekeeping' definition of negative carrier, not the 'clear-topped device placed under the enlarger for easier contact sheet making' definition.
9. Don't be afraid to experiment. Experiment with different shutter speeds for those cool 'part of the picture is sharp and the other is motion blurred' effects. Try reticulation. Try solarization. Line up your shots. Enjoy.
10. Show the dancer of your choice their fabulous close-up shot, THEN ask them to dinner. And when you're there, don't chew with your mouth full.