Amend some of the tips as appropriate. I wrote this with a stage play in mind.
Logistics
1) Permission - get clearance from the director, and that the theater director knows that you have clearance, or arrange for the staff/ushers to be informed. Besides being a matter of professional courtesy, this would save you a lot of grief. Also, getting permission form the Director(s) can sometime mean getting access to areas normally shut off to members of the public/audiance. Be sure to thank those who assisted, and if you feel so inclined, pass them a nice 8x10 glossy of the closing line-up, or a key high-light of the performance as a gesture of appreciation.
2) Location - If time is not of the essence, go ahead of a perfromance and scout the location. Try and get permission to pop by in the afternoon and really scrutinise the location. Everything from strategic locations in the ailse, wings, sides of stage, and even lofters can offer advantageous shooting positions. Some of these may offer you the option of a less intrusive position.
3) Plan ahead - Attend a full-dress reharsal or a performance ahead of your shoot schedule. Bring your camera along and try to meter ahead just to get a feel of things. Shoot if possible.
In the past when I shot all film for stage, I would go ahead to scout, attend a few reharsals, take incident light readings for the 'must-have' highlights of the performance and do at least one test shoot. I place great importance on point #3, but the most important still remains #1.
Equipment
4) Lenses - Chances are, unless you get permission to shoot from the wings or lofters, your 50mm and 85mm would be your most used lenses. Be prepared to go high in the ISO settings, and use noise reduction softwares if necessary. Refer back to #3 and you'll see why attending a reharsal/performance and trying to get some test shots is important.
5) Support - A lightweight, easily set-up BLACK tripod with a quick detach (that's not noisy to set-up; some are!) is a lot more versatile than a monopod. A tripod can easily be used as a mono, and with a lightweight set-up, you're good to go. Also, it's easier to leave a tripod standing as opposed to laying down a mono, and possibly forgetting where you left it. The number of keepers with some kind of support increases dramatically as opposed to just hand-held. Consider 'bean-bag' type supports, but you'll only know if they would be useful if you do #3.
6) Shutter noise - As silly as this may sound, drape one or two black or dark, THICK towels over your head and camera. This would muffle a bit of the sound to a level where only someone just beside you would barely be able to hear it.
7) Attire - Wear ALL BLACK. This would decrease your level of audiance intrusion when you move around during the actual performance. Also, wear sneakers or any rubber soled shoes. Depending on the level of formality of the whole affair, normally, blending in might make you feel more comfortable, but if it's a formal affair, then you have to get yourself comfortable working in that attire.
8 ) Visibility - Since you will most likely be working in the dark most of the time, be very, very familiar with your equipment, and practise changing lenses, settings etc in the dark/low light. Carry a low-powered blue or red coloured LED torch to assist when absolutely necessary.
9) While not directly related to the logistics, get familiar with the body language of the conductor and key performers (the ones who do solos). That would put you in a position to identify, and prepare to shoot award-winning moments and expressions.
10) Have fun!
Basically, I would say that while all points are important, #1 #2 and #3 are the most crucial to success.
Hope this helps some. I may have missed out some small, but terribly significant pointers. Please feel free to add-on and that would be feetie dollar marnie take come. Thank you.
CHEERS!