leave the theatre promptly but not before bows are completed (that would be rude)
be accommodating to your fellow fans - if someone is behind you, offer to pass their item forward to be signed. I do this any time there is a crowd and it is always appreciated. If you can, shuffle around a bit so people can get a photo, I usually say something like "I will switch spots with you so you can get a photo, provided you switch back right after so I don't lose my place"
Be respectful to actors. Don't be weird, don't be creepy, don't act like you're their personal friend or spend twenty minutes talking at them when they want to go home.
Usually I hand them my playbill/item, and while they are signing it give a specific compliment or question. Or hey if I wasn't jazzed about their performance just say something like "I really enjoyed the show!" But if you can, specific compliments on their work like "Oh man when you hit that high note in [song] it was amazing" or "your dancing is incredible, it really stood out to me" "That moment when [plot happened] and you [reacted], it was so gut punching and real".
And you will already know this, but just be respectful in general. If sometimes doesn't feel like signing, or only signs for a few, or will sign but not take photos, be happy with what they choose to give you and spread that attitude with your fellow fans. It's a gift!
But in general, yeah, relax. Stagedooring is mostly a lot of waiting and then trying not to say something dumb to someone who has heard a million people accidentally say dumb things to them already. Even if you don't know what to do, they know the drill.