First, you'll want a tripod for your iPhone. I use this little $6 bracket, combined with a run-of-the-mill $2 mini-tripod. Other people have had good luck with more professional solutions.
Next up, you'll want KitCam. Buy it for $3 and install it on your phone.
Now, you'll want to configure your phone so that it's ready to shoot an improv show.
* Make sure you have a decent amount of space free on your phone.
* Go to Settings and put your phone in airplane mode.
* Launch the KitCam app.
* Press the gear-icon button.
* Press "Video" in the resulting menu.
* Touch two fingers to the main screen area.
At this point, the app should beep and show you two shapes: a blue square and a yellow circle. The square is for locking focus. So aim the phone at the stage and click the "refresh" icon in the square to lock the focus -- the "refresh" icon should change to a padlock icon.
The circle is for locking exposure. Get someone to stand on stage under normal stage lights. Aim your phone at a light souce -- the upstairs theater at the Hideout has a desk lamp that's really useful for this -- drag the yellow circle so it's right on the light, and press the "refresh" icon in the circle to lock the exposure. The "refresh" icon should change to a padlock icon.
Now, try aiming the phone at the person onstage. Is that person visible, or is it too dark? Is their face visible, or is it washed out from overexposure? If the exposure is mis-set, press the padlock in the yellow circle to switch it back to the "refresh" icon. If the exposure was too high, bring your phone closer to the light source and re-lock the exposure. If it was too low, aim your phone at the light from further away and re-lock the exposure.
Once you home in on the correct exposure, put the phone on the tripod (if it isn't already) and aim the phone at the stage. Ideally, you'll want to aim it *between* two adjacent seats of the back row, so you don't wind up with some macrocephalic goon sitting directly in front of your phone.
You can adjust the (digital) zoom at this point by touching your finger to anywhere along the bottom of the main screen area. This should make a 'zoom' slider appear, which you can then drag left or right.
At this point, you should be able to hit the "record" button and let it run for the duration of the show. When the show is done, hit "record" again, and ta-da! all finished.
Afterwards, you can click the small, square picture to the far left of the record button to get to KitCam's camera roll. Find your new recording in that list. Press your finger to it and hold your finger down for a bit, and some buttons should appear at the bottom of the screen. Press the 'box with an arrow pointing out of it' icon in the bottom left corner and a menu should appear -- one of its options will be "save to camera roll". Press this button, and KitCam will copy your new video to the iPhone's main camera roll. Now you can easily copy your new video file to your computer.
 The iPhone's built-in video app sucks -- or rather, it's perfect for people who want to shoot one-minute videos of their kids playing in the park; it sucks for shooting videos of improv shows.
 I like to leave at least 6GB free. An hour-and-change show is usually about 3GB, and I wind up making an extra copy of that file when I transfer it to the main camera roll.
 With the built-in video app, if someone calls your phone while the app is recording video, the app immediately stops its recording. I don't yet know if KitCam has that same "feature", but I don't take any chances.
 You would think that just letting the phone automatically set the exposure would work fine. For some reason, stage lights confuse the iPhone, and it always sets the exposure way too high (nobody has faces).
 You might also think the 'manual exposure settings' in KitCam -- the ones you reach by hitting the +/- button to the right of the record button -- would do the trick. Unfortunately, they don't; that just controls a post-processing step that digitally bumps the brightness up or down. (So, if you turn down the manual exposure setting, nobody has any faces, *and* they look a bit darker.)