Choose a location where your animal will be relaxed
Get (down on) eye level with your animal
Minimize (remove) distracting things in the background
Generally, the more (natural) light, the better, and typically having the light source (the sun) behind you makes a better photo, too
Photograph against a color that contrasts with his/her coat (I.e., if your animal has dark fur, photograph against a light background and vice-versa)