I'm taking a Go Pro to shoot some diving video, and I've never done this before. Assuming a mask mount is not an option, would you strap it to your wrist, attach it to your BC, or take it loose / on a lanyard with some sort of short pole? I've seen floatation mounts - are they recommended for diving?
GoPros have quite short battery life and it's not possible to change the battery under water. Therefore you'll need to turn it on and off. The best place to hold a GoPro is in the hand as you can frame the shot and hold it steady. Attaching it to a helmet / head strap results in lots of poor video which you'll probably throw away.
Lighting is key to good underwater photography and GoPros aren't that good in really low light, e.g. UK diving, so you'll need additional lighting that is very wide-angle. The best lights are very expensive; many times the price of the GoPro camera.
I accidentally flooded my GoPro by failing to properly close the housing -- an expensive mistake. However, as an unintended consequence, my diving massively improved as I now enjoy the dive and not taking endless awful quality video!
It's a Hand grip, which is inexpensive and easy to use. you can attach it with the band to your wrist. That means you can just let it float if you don't use it at the moment. Then when you want to use it, just grap it again.
A head mounted approach is easiest and shows people your POV (point of view), bubbles can be an issue depending on your reg and swimming position. But greater risk in losing it of your head. Some people hard mount it on a plastic type helmet (cycle/caving/construction) and then attach the helmet over their hood.