It's important to communicate what you want to the handlers. A lot of people give up too easily. They don't think this leaping maniac is ever going to calm down, but they usually do, and you usually can get a good picture if you take some time. You can't get a good picture without it. We are discussing making good portraits of animals to help them get adopted.
Animals are the subjects of our photographs.
However, the dog or cat does not fill the entire frame of the picture. What happens in the rest of the picture will either help to show off the animal or will distract our eyes. The background helps make the picture a portrait instead of just a snapshot. Look for a neutral background, usually in the mid-tones, that is more like gray than black or white. Something with texture is good, but avoid something that is too busy.