Try and take your photos from the eye level of your pet. These make the best angle for a portrait. Shots taken from above looking down on your pets can be unflattering and usually don't work well. Try kneeling down, while holding a treat or speaking their name. A 3/4 head angle works very well for a portrait. 

Lighting is very important in any photography and Pet Photography is no different. Good lighting allows for accurate fur and eye color. A soft, natural light sets the whole tone of the portrait. Sunlight -not direct sunlight- works best. I recommend having you pet sit next to window with the light hitting your pet from the side or straight ahead. Avoid light from behind - though this can create very dramatic photos, it is often harsh and casts the subject in shadow.

Successful pet reference photos show the fur direction and clear eye color details. As a rule of thumb, if you can see the details of the fur and eyes when taking the picture, it's a good bet the photo will too. This really helps in getting a good likeness of your pet.

Don't feel you have to pose your pet for the photo. Most often, the natural look and expression of you pet works best. After all, it is this that represents your pet most of the time. Try getting some shots while they are laying down in "their spot" or on their favorite blanket, or spot on the couch. I know, they are not allowed on the couch, but who are we kidding right?!? 

All of this goes a long way incapturing your pet's personality.