After misc. paperwork and getting fitted with a harness, you pile in to a six-wheeled "army vehicle" for a short drive over dirt roads. Our great guides for the day, Todd & Dan, did a safety briefing and said lets go zipping. One of them goes first, and then the other safety checks each person, clips us in, and sends us on our way across the canyon. One naturally "holds on" for dear life (similar to parasailing or sky diving), but you are in a harness and my younger son started doing hands-free hot-dog moves! By the last ride, everyone was relaxed and enjoying the awesome ride, view, and experience.
The self-portraits were kinda fun as Todd & Dan were willing to bring an extra "zip line runner" that we attached in front of me. I then screwed in a tripod mount to the Canon 50D DSLR (with an ultra-wide lens on it), put a carabineer through that, and attached to the runner. I could then reach up and trigger the shutter. Remember this was my first time ziplining, so my natural inclination was to "hold on", but I was careful not to yank the camera, especially since I "sagged" when I started zipping. This resulted in a steep vertical angle, so after a couple of runs, I asked if we could run a rope to drop it a bit and they were happy to help out. This worked much better, plus I was getting more comfortable in the harness/zip line. Even with the ultra-wide lens, I was a bit close since my arms are only so long. Another approach would be to put the camera on the tripod (with safety straps) and have that hooked up to the runner to provide about another foot of offset (about all that you would need) and use a wireless trigger to fire the shutter. Or optionally, run a second (better looking!) person down the zip line next to me and simply have me take pictures of 'em as they go down!
So lots of different ways to shoot this, but it was my first time zipping, plus I wanted to enjoy the experience. Would be fun to do it again sometime!