I've been reading up on this alot lately, so here's what I've learned so far. I'm assuming that you're using a digital camera which means you have to overcome shutter lag and next shot delay.
Shutter lag is the amount of time between when you push the shutter release and when the picture is actually taken and can be up to several seconds. Next-shot delay occurs between shots when the camera is writing the image to the flash card and is usually longer than shutter lag.
You can combat these a number of ways:
* Decrease shutter lag by focusing the shot before you take it by pressing the shutter release halfway. This focuses the camera and prepares it to take a shot. When you press the shutter release the rest of the way, it takes the picture.
* Disable red eye reduction. It really doesn't work for animals very well anyway and greatly increases shutter lag. You can always use software to remove it after the fact.
* Many cameras have a sports or action setting. If your camera doesn't have this then you can manually adjust the aperture and shutter settings. Not only does this help your shutter speed, but it also eliminates the blur from movement.
* Consider using the burst mode. This takes a series of continuous shots in a row. This is great for pets who can't sit still.
I especially like these last two but the downside is that you can not use a flash with these settings. I don't like using a flash anyway because it distracts them and makes the next shot hard to take. Not to mention you get the spooky eyes. I always like to use natural light so I either take the picture outside or next to a window. I really like the shadows that using natural light indoors can create too.
Some cameras let you take video. This is great for catching action shots if your camera will let you move frame by frame after you take the video.
This link has great tips for taking pictures of pets.
http://digital-photography-school.co...otograph-pets/
Here are some of my pictures. The first one is inside using light from the window to create great shadows. The other two are outside using natural light, props, and different types of framing.