A theater major with an assignment to do? High school student doing some extra credit? You don't need to be a professional theater critic to insightfully critique a play. Here are a some useful tactics you can employ to help earn you that A+.
Prepare yourself. Eat and use the bathroom beforehand so that you won't be distracted during the show. Bring a booklet or notebook and pen for note-taking. A dark blue or black pen works best because in a darkened theater, with only the stage lights to help you, pencil on paper will be almost invisible.
Note-taking. Good note-taking is going to be key, especially if you're not used to writing critiques. The more information, the better. Go through the cast list before the show and familiarize yourself with the characters. When taking notes, write only the first two letters of the character's name so that you will save time. Don't forget the program when you go home so that you can remember the actor's names.
Don't let the interpretation of the play affect your critique. A play can still be fantastic even if it's unlike what you had in mind. Look at the more technical aspects (both in acting and in the actual tech theater, i.e. lighting, set, etc). See if these things fit with the interpretation you think the director is trying to present. If you disagree with the interpretation, write about it, but don't let it affect your judgement of the skill of the actors.
When note-taking start with the actors first. Later, if you find you didn't take enough notes on the acting, you'll have a hard time remembering each actor (especially if it is a large cast). Once you feel you've got a good hold on the acting, take notes on set and lighting. Sometimes the curtain is up before the show starts, the set in view. Take notes then, to save yourself time during the show.
Organization. In your paper, you're going to want to go over all aspects of the show in a systematic order. There is no specific order you need to stick to, as long as your report is coherent. For a shorter paper, focus on main actors only unless there is a significant note you want to make about secondary actors or the chorus. Always refer to the actors and not their characters when critiquing the acting. The review isn't about what you thought about the play (the actual written play) but the presentation of the play, the show itself.
Pay attention. If you're not used to play-going, sometimes shows (especially poorly done shows) can be boring. If you want to write a great paper, you're going to need to pay attention regardless. Try not to zone out and watch the show as closely as possible. If it isn't a specific play you're required to see, try to get tickets to something you'll enjoy. It'll make the experience less tedious.
Read other critiques. To get an idea about how to write a critique, read one. Try not to read a critique about the show you're going to see and if you do, don't plagiarize You want your paper to be your own.