The Kitten's Tale

If anyone had told me years ago that I'd be photographing kittens with flowers I'd have told them they were mad... and yet here we are. Thing of it is, animals - and small, highly mobile ones in particular - present a special set of challenges to the photographer.
Humans don't always like sitting for a portrait, so an important part of any portrait photographer's job is to relax their sitter and help them enjoy the session - it will result in better portraits. Animals are the same, except you can't unleash your best jokes on them and expect them to fall about laughing.
So, rather than a bagful of witty one liners, approach a pet portrait session with a suitcase full of patience. Have your camera ready and watch your pets play, waiting for just the right moment to shoot. The noise of the camera may well attract their attention. If so, snap another quick shot for that 'eye contact' look.

When photographing small animals, get down to their level, and get in as close as you can without distracting them from their fun. Think about what is in and out of frame; try to include elements that help tell a story - after all, for 32,000 years visual art has been all about telling stories. If something makes for a distracting or irrelevant element, whip it out of shot, or crop to exclude it.
One of the biggest distractions in home-shot images can be the background. Houses tend to be cluttered with furniture, ornaments etc. If you are planning a photoshoot with your pets, have a bit of a clear up first. But you cannot clear away everything, so try setting your camera to a wide aperture - maybe f5.6, or even wider - f3.5 or f2.8 - to blur out the background. Depending on how close you are to your pets, you may blur parts of them too, so make sure you are focussing on the most important part of them, usually their faces.
A wide aperture will have the added benefit of allowing you to use faster shutter speeds. This can be very handy with kittens, for example, who rarely stay still except when asleep. The faster shutter speed will stop or reduce motion blur. You might also consider setting your ISO higher to further increase shutter speeds.

If your camera offers a range of metering options, and lighting conditions are contrasty (lots of very light and very dark areas), try the spot metering mode. Make sure you are metering from (i.e. focussing on) your pet, rather than the background. That way your pet will be exposed correctly, and if the background is too light or too dark, it doesn't really matter - it can even look quite nice, as over- or under-exposure of the background will remove more unwanted distractions.

 A word about light sources. Natural is best. Your camera's flash can do a job, but will distract your pets, and also flatten the image. The image will probably be sharp as the flash will freeze motion, but it will also lack character. The image below is an example. Harold and Maude still look cute, but the other images in this set possess a lot more character, I hope you agree.

If your home is not the lightest (as many are not at this time of year), you could put your house lights and lamps on to supplement any window light. However, be aware that in most cases this will introduce colour casts to your images, and they can be tricky to remove entirely when you have different types of light in the same image.

 
Lastly, don't get frustrated if your pets don't strike the pose you were hoping for, or if you just miss some 'money shots' - it happens to the best of us, but if you remain chilled your pets will too, and they'll be sure to present you with another opportunity for a cutesy classic.