I've tried photography animals a few times, the best was when I was at the zoo last week. Pretty much take your pick of what animal you want to capture.
For me this was the tigers. I would suspect that taking their picture would be simlar to any other animal.
They were always on the move, so I tended to wait for them to turn around and come down towards me (I was behind glass so was pretty safe). I switched the camera to multiple burst mode so that I could capture them while running. This one below was probably the best one that came out.
Flickr - Tiger
My advise would be the same as others, get in close and take as many pictures as possible