A performance could be anything from Kathy Fincher creating her art in the middle of a fundraiser to bareback riders at the Circus.
What I like about shooting a performance is the theme is instantly recognizable and it informs us about an interesting part of the subject’s life.
I wanted a picture of an elephant, so when the circus came to town I got a ticket. It would be hard to find people and an elephant interacting this way outside of a Ringling Brothers show.
The first thing is to ask permission, because unauthorized photographers can be asked to leave (as in RIGHT NOW, JERK!!). Most professional productions forcefully guard their copyright and only allow cell phone camera pictures. The Barnum & Bailey Company was an exception. They encouraged the audience to come on stage and fill the three rings before the show and to continue taking pictures through the evening (strictly with a 50mm lens, no telephoto). It helped to be in the front row.
Secondly, plan to shoot without any type of flash. That means a high ISO setting (1,600 in the picture below) and dealing with digital noise. Anti-noise software helps but is not perfect. Expect to produce 4x6 images without excessive crops. That is good enough for a 5x7 picture card.
If you can get access, dress rehearsal is a great place to shoot.
Most non-professional companies allow friends and relatives into dress, and you may be able to freely roam from front row to balcony. Don’t expect to shoot from the wings (a unique perspective) because of all the traffic there.
My last consideration here is color control: we always want flesh tones to be realistic. That can be a problem because theatrical lighting is sometimes deliberately unrealistic, and usually there are multiple sources with different characteristics.
Fortunately, we are accustomed to unusual colors in this situation and they are appropriate as long as we avoid the repulsive. If the color is too weird but the composition is otherwise strong (the purple legs, below), consider a B&W treatment.