Pet photography is quite an art in itself. The photographer ideally would love animals and have a raport with them. If you head to The Pet Directory website you will see lots of pets in many different photos with a varied use of animal photography.
Sometimes it is of value to take a pet side on or as with purebred dogs in what is known as a stacked position to show conformation. For appealing pet photos it is best to have the dog, cat, bird or other pet looking at you in some fashion so that the photo shows the nature of the animal, its essential spirit.
Pet photography takes a lot of time and patience because the subject moves! Often the owner is a big problem because they continually gain the pet's attention fussing around it thus spoiling the chances for the professional photographer of getting on the pet's agenda.
Lots of practice and patience is essential and it is one case where taking lots and lots of shots will probably reap you a couple of good ones!