Arrive early to the theatre/venue, preferably fifteen minutes before seating begins.
Step2
Find an usher or box office attendant. Ask them where the stage door is. Follow their directions and find it, just so you know where it is.
Step3
After the show lets out, head to the stagedoor.
Step4
When you greet the performers, do not refer to them by their character name. Definitely don't refer to them by the wrong character name. Ask them politely to sign whatever you've brought, and/or take a picture. Do not shove things in their faces, scream, or grab them. Don't expect them to spend an hour with you (although, there are some actors who can talk for hours at stage door. Most keep it under a minute, though).
Tips & Warnings
Do not chase an actor down the street.
Actors come out at different times. Some are out the door within two or three minutes of final bows. Others can take over two hours.
Try to find people who have seen the show or met the actors before. They're usually more knowledgeable about individual performers' habits (i.e., who sneaks out, who can chat for hours, etc.).
Have fun!
You may not catch all of your favourite actors, as some venues have multiple exits. Contrary to popular belief, actors are not obligated to stage door. It's a nice thing that they do.