Most people don't photograph alligators in the wild. They go to zoos or theme parks (like the one where this one was taken). I'm blessed with the opportunity to live very near some of these dangerous creatures. This is NOT the time to use tripods. They are typically found near the water.
For every one that you see sunning themselves on the bank, there is at least one hidden from view in the water or vegetation nearby. In the area where I live in Florida, it's not highly populated and the alligators are not used to tourists coming by to photograph them.
Most of the time I take the photos from the hood of my car or from inside. For the ones that I'm familiar with, I'll sometimes get out and (staying at a safe distance) photograph from a squatting position, but only if someone else is posted as look-out. I've been nearly caught once because we didn't see the gator that was in the water while we were photographing the one across the bank. I've also had gators lunge across a ditch at me. For huge reptiles, they have amazing speed and can go from a lying down, seemingly asleep position to a ferocious predator at your feet within a micro-second.
Anyone else here photograph alligators in the wild? I'd love to hear your stories.