Right now, I video shows with my iPhone 4. I have a small plastic bracket like this one, which sells for about four bucks. I also have a bendy-legged mini-tripod for it to sit on, like this one, which sells for about two bucks. Typically, I put the tripod on the 'windowsill' of the tech booth, aim the iPhone at the stage, plug it into a charger, hit 'record', and go.
There are many drawbacks to using an iPhone to record your show. Video and audio quality are not the best. For some bizarre reason, the phone cuts out at fifty minutes and says it can't record any more. And there is still no way to manually crank down the exposure level on the video, so half the time it goes for a really wide aperture and blows out everyone's faces. (There's a chance that AlmostDSLR could fix that difficulty.) Also, you absolutely want to put the phone in airplane mode, since any incoming alert will shut off the recording, and you'll want 3-4GB free for a 1½-hour show.
I may move on to using a Zoom audio recorder in the future, just to get better sound with better mics from closer to the stage. And I might even buy a proper camcorder -- Brad has had good luck with his Canon Vixia HF M40, whereas Paul Normandin opts for the R20 with good results.
Me, I'm keen to hear any & all advice.
 "Someone texted this phone FOR GOD'S SAKE STOP TAPING THIS!!"