Here are some things I try to do when I'm photographing dogs:
1. Bring an assistant, toys, and dog treats - I often find that I don't have enough 'hands' to be able to get the dogs attention, direct their looks (as best I can) and also be looking through the viewfinder, composing, and taking the pictures. An assistant can help take some of the jobs off my hands so I can concentrate on getting the best shots possible.
2. Wear 'em out - I generally advise owners to wear their dogs out with a good walk, or whatever their dogs favorite activity is (chase, tug, wrestle, etc.) before the session. This helps the dogs to be more docile during the session.
3. Add some time - Generally I try to give a half-hour before the session actually begins to 'bond' with the dog(s). I want them to get to know me and my voice, the environment where the pictures will be taken, etc. I often will take dogs on a walk (thanks Cesar Milan!). I also let them 'explore' my equipment by showing them everything and letting them get their curiosity out by sniffing it... Once they know the smells and realize that the equipment isn't edible, they often lose all interest in it completely. Keep your lens caps on unless you want doggy nose smudges on your lenses, though! I find this can really help dogs to relax and can make them less curious about every little piece of equipment as I fiddle with things during the session.
4. Careful with Strobes - If I can, I try to avoid strobes as the whine of them recharging can really cause problems. If I am forced to use strobes I do try to fire the strobe(s) a bunch of times in the dogs presence before the session begins in order to help them get used to the strange noise...
5. Bring leashes! - If the pets are really fidgety it can help get them into position. You can then edit leashes out in post... Or not. Usually I don't bother because people generally don't mind having their pets on leashes in pictures.
6. Use a long zoom lens - I usually shoot these sessions with my 70-200mm lens from relatively far away and cranked in to between 135mm and 200mm. This gives me the chance to get relatively nice bokeh without necessarily having to open up the aperture up all the way.
7. Try to take the pictures in an environment where you've got a a lot of depth behind the dog(s)/subjects - I'll often do these sorts of shoots at parks, or in a backyard because having a lot of depth behind the subject allows from more possibility for a nice bokeh without having to crank the aperture open so far that you end up with lots of out-of-focus shots because the dogs are wiggly.
8. Invite the owners... Maybe - For dogs especially they often are more in tune to their owners voices, know their owners commands, know their owners expectations, etc. This can be of great benefit as long as the owners understand that their job isn't to yell commands at the dog ('Look over here, Fluffy. Fluffy! FLUFFY! LOOK HERE! HERE, HERE BOY, HERE!!!') These sorts of histrionics can often serve to either make a nervous dog even more nervous, or an excited dog simply uncontrollable. If an owner is simply unable to control themselves and speak to their dog with a normal tone of voice throughout the session I will generally ask that they 'give us a few minutes' to take some pictures without them around. The vast majority of the time these turn out to be the best pictures of a given session.
While 95% of the pets that I've ever photographed have been either a dog, a cat, or a horse, on occasion I will get asked to photograph other types of pets. In terms of other 'higher order' pets (horses, cats, etc.) with the possible exception of item 2, all of these tips will apply more-or-less as-is. For smaller pets (ferrets, rats, hamsters, turtles, snakes, etc.) no amount of preparation will help, so items 2, 3, 4, and 8 generally will apply less (or not at all), and for the most part you will be taking pictures of smaller animals with their owners, so the shoots become less about the animal and more about a standard portrait session with the owner holding their pet.
As an aside, most of these also work great when photographing kids. Except for maybe the leash thing... On the other hand... ;-)
