If standing, they should be profile to the camera, in a natural balanced position that shows all 4 legs, head turned part way to camera. Lieing down is my least favorite, but ocasionally works. Get as close as possible to eye-level with your subject. Put a cat or small dog on a table or something so that you don t have to lie on the ground. This is important.
Amateurs frequently photograph everything from a standing position.
Looking down on a dog or cat is not a good way to best show who he is. Treats and squeaky toys do not work that well with shelter dogs. The excitement of the moment is more powerful than treats. It's important to communicate what you want to the handlers. A lot of people give up too easily.