Pet photography is one of my favorite things to do, and one of my favorite models is my dog Marley! Here are some thoughts on photographing your pet to make it fun and non-stressful for you both!
First, a thought about the stress part. If you are planning to do a "posed portrait session" with your pup, or kitty, or goldfish ... forget about it! Their attention is fleeting, movement quick, and more often than not, you just won't be able to keep up. Instead, think about it as you entering their world as an observer; snapping candids of them as you can. Now you certainly can set up these situations by making available their favorite toy, or engaging them in one of their favorite activities, but the idea is that you want to photograph a happy pet engaged in something they love.
To take the best pictures, you have to be ready and quick with your camera. Anticipate your shots and fiddle with the settings ahead of time. I almost always want a fast shutter speed to freeze the action and make it more likely that I will get a shapely focused shot. Similarly, I am more likely to use a mid-range aperture like 5.6 to give me a moderate depth of field when the action starts. And by all means, have the autofocus on.
Pick a surrounding that has good lighting ... not harsh lighting ... good lighting; I prefer to take pictures earlier or later in the day because then I can avoid light with harsh shadows. It's also not a bad idea to use the auto-ISO feature on your camera at these times to increase the likelihood of an correct exposure. You get the idea ... it's all about capturing the moment, not orchestrating it; so you have to make sure your setup maximizes your odds. Second in importance to lighting, is the nature of the setting . An uncluttered background is best, so the attention is drawn to your subject.
My favorite shots are of pet expressions... just like people. Get down low to capture these shots and have a few things up your sleeve to get your puppy or kitty or whatever to look at you. Perhaps a squeeze toy or a kazoo to make that unique sound that captures their attention for the moment . I will often shoot in burst mode for the very reason that it ups my odds to get a terrific expression.
As a final thought, it's great to capture pets and people too, although it can be even harder to get the animal's attention in these situations , but interactions between animal and human can be priceless. When photographing a person with their pet, shoot with as large an aperture as possible to blur the background, and do your very best to fill the frame.
T here is nothing like the innocence, play, and love of a pet to make us feel warm and fuzzy all over. Go capture some!