Here we present, in unmitigated splendor, some of King Pup's many cherished doggie friends from the past and present! Click photos to enlarge.
Photographing an animal from their height, instead of looking down upon them, makes the difference between a mediocre pet photo and a great pet photo.
Try and avoid using a flash wherever possible. They can startle your pet and usually give mediocre results. Natural light does a much better job of bringing out their natural tones and textures.
If you're taking a portrait of your pet, you may find it next to impossible to get them to face the camera long enough for a good shot. Try calling their attention to their favorite toy. Simple, but it works!
Since animals have a shorter attention span than (most) humans, it's hard to get them to pose. Dogs are easily distracted by movement around them and so it's likely they will move their heads around a lot, especially if you're outside. Just go ahead and take as many shots as you can, you'll usually find that one catches them "just right!"
Shift the focus away from distracting backgrounds and fill the frame with your pet's face. They are, after all, the subject - and a close up shot will really bring out their natural expression and the texture of their fur.
It makes all the difference if you have a friend to help you photograph your pet. They can hold them in place and use distraction techniques while you focus your attention on the camera.