When shooting your pets its a great idea to shoot a number of photos. If you shoot a few horizontal and a few vertical, and shoot at different times of the day (especially with light coming in the windows) you′ll find you get better results. Try shooting the pet from a number of different angles and camera positions.
Get in close. Many people photograph their pets from too far away, include the whole back yard when they really just want a photo of the dog. You should shoot a wide shot or two but get in tight on the pets face for a couple of frames.
You will also get better shots if you avoid using the flash indoors. The flash makes the light look harsh in this type of photo. You′re better using natural light when shooting pets. Try opening window blinds, and turning on all the lights in the room in addition to using a higher ISO to shoot without flash.
Cats are easy to shoot if they′re napping (they are generally lazy so its not too difficult). Dogs often move around a lot more and you may be better photographing them outdoors where there is more light.
If you are shooting with a limited depth of field (f4 or less) focus on the animals eyes. If the eyes are in focus the rest of the pet can be a little soft focus and it still looks good (sometimes better).
Change your perspective, get down to the animal eye view, at eye level with the pet. In this photo the camera was slightly below the cat and looking up. This makes much more of a connection in the photo than if you were standing up and looking down at the cat. It also makes for an interesting background.
This photo of the cat with the family was shot by my wife Tracy Adler who is not a professional photographer. Its a really good photo because all the elements came together. The focus (literally and figuratively) is on our son, Luke. But the cat is fully in the photo. A lot of people would have cut the cats head off in the framing when taking this shot. Try to see the whole photo when you are framing, look at the edges as well as the middle of the frame.