In almost all shows, you will come in entrance doors on one side of the theater and if you need to exit, the exit doors will be directly across the theater from the door where you came in. Usually, the CM introducing the show will mention where the exits are. They are also marked with an Exit sign. Even if they appear to be closed or have no handles, pushing on the door will open it.
Just remember NOT to try to leave from the same door you came in on. There will be a preshow or waiting area full of people waiting for the next show right outside those doors.
If you think you might need to leave during the show, it might be good to sit toward the back and continue all the way across the row of seats to the end opposite where you came in. That way, you will be able to leave the most easily.
Once you leave, it will not be possible to come back in - the doors have no handles on the outside to open them. Since most shows are not very long, the chance of finishing what you need to do before the show is over is not very likely.
It is not possible to leave Carousel of Progress, Ellen's Energy Adventure or any rides without triggering an emergency shutdown.
As was mentioned, there are a couple of shows where you need to contact a CM before leaving for your own safety and the safety of the performers. They will mention that before the show starts in case you forget which attractions they are. But, the only ones I can think of are Nemo, the Musical and Lion King. Even though you may not see them, there are CMs stationed inside of shows to help people who need to leave.
For Fantasmic, the theater will be darkened during the show, but if you need to go out, you don't need to exit the area. There are food stands and a set of restrooms at the back of the amphitheater area. You could just leave the seating area and head towards the restrooms.
Whenever you leave a show, just make sure to arrange where yo meet back up again with the rest of your party.
