The most important thing in taking photos of someone's companion animal is to capture the emotions of the animal. Not as easy as it sounds, because most dogs, under these conditions, will be curious, happy, running about, etc. It's sometimes hard to get anything other than the goofy, tongue-hanging-out face from most dogs. But the longer I spend sitting with the animal, playing with it, talking to it, etc., the more likely I am to get a wider range of emotions when it's time to start shooting. The whole idea is that the dog (or cat) isn't aware that anything has changed.
I love this shot of Lola, because it's so clear that she didn't want to model for me on this day. I rarely see her upset, so this shot is a big treat for me. Not because I pissed her off, but because she looks so silly trying to be a snot (because honestly, she's not one.)
