Is harder than you would think. I know a guy who specialises in pet photography and he must be a mixture of lighting technician, sports photographer and saint.
For a start, pets are usually smaller than people. This means you need to get close, but you also need to get low to be nearer their level (and besides, dogs can’t look up). But close means shallower depth of field. And since pets are often arranged horizontally rather than vertically the fall-off in sharpness may be more noticeable.
Fur also soaks up light. I’ve got some pictures that include a black dog and it might as well be a hole in the film.
Flash can still be useful, as the buggers won’t keep still or pose. You have to watch out for highlights in the fur though, as it can be surprisingly glossy. Think of your subject being a mixture of Vantablack and mirrors.
You also run the risk of startling the animal. One time I was shooting someone jumping fences on their horse. I so wanted to use flash to get a bit of light into the subject and freeze the motion, but I was advised that startling a horse mid-air while standing that close was a bad idea (still not one of the ten worst things though). Dogs and cats (and many others) have also got reflective retinas, meaning their eyes light up like a zombie apocalypse if you get the angles wrong. But if you don’t use any lighting you can lose the catch-lights in their eyes and make the animal look like it was stuffed.
The best lighting seems to be big, soft sources like a large window. It means you can see the detail in the fur and the eyes.
This is where digital wins totally over film. You can shoot hundreds of pictures and review them instantly. You’ve got autofocus. You can judge the exposure right off the back of the camera.
Or you wait until they are asleep.
And even though I wouldn’t want my mate’s job, at least it’s not shooting weddings.