Do your research. If you're going to see a classic play, read it before you go so you can discuss it afterwards. If it's a new play, research the playwright to see if he has any new plays coming out soon. You might be the perfect fit for that next show.
Read the program. When you're sitting in your seat before the show begins, read everyone's biographies and study what they look like. Concentrate mostly on the director's biography. Chances are, if you've been in the business for any time at all, you will be able to converse about something the director worked on in the past. It's much more important to create a relationship with a director than with other actors. Other actors aren't going to hire you. Directors will.
Pay attention to the show. Notice what the director did with movement, the text and his casting choices. Figure out the director's taste, and remember a few moments you particularly liked about the production. Once you can speak to the director face to face, you can show your genuine interest in the specifics of the production.
Bring your headshot, resume and business cards to hand to the appropriate people. These include the director, casting director, stage manager and any office personnel who might attend the show. Office workers can sometimes pass your information along to the director. It's absolutely acceptable to stay in the lobby after the show to congratulate the actors and meet the director if he is there. Don't linger too long, but say your thoughts clearly and politely. Offer your business card first, and your headshot and resume only if requested.
Stay in touch with the director, playwright and casting director after the show. Write a short cover letter explaining who you are and how much you liked the show. Also, tell them a few career achievements of your own, as well as what projects you'd like to work on in the future. Tell them you would love to be a part of their next round of auditions. Attach a headshot and resume if you haven't provided these already. Thank them for their time and consideration.