Try to be on the eye level of your subject. Especially smaller animal need to have you on their level to have a good shot without distortion. These photos were taken inside with a digital camera. For multiple animals, take individual photos and I can seam them together into a single painting as I did here.
Take several shots of you pet's face as it will help in getting its expression and most importantly, the eyes. You may need help from another person holding a toy or a treat for distraction.
Try not to use a flash as it can sometimes cause an altered color or red eyes.
However, even a bad photo will work. As shown below I have salvaged this old photo into a small painting.
Get outdoors if possible on a bright day or a hazy overcast day. This light will be great for a good photo. If this is not possible, go near a window with the natural light on your subject's face. If you are fortunate enough to have a digital camera, the results are usually quite good. These photos may be emailed to save time and expense.