I echo the thanks to johan rebel and JDiver for the incredibly useful information.

One thing that befuddles me is how to convince the autofocus that I want to focus on the creature in the mid-ground, and not on the grass or brush in the foreground. Here is an example of what I'm talking about: when I press halfway down on the shutter, the focus box/boxes appear to be on the zebra, but in fact they're focusing on the twigs in the foreground. I'm using a Panasonic FZ5, probably set to automatic shutter speed and focal length.

Suggestions, tips, etc?