Naturally the shutter speed must be fast enough to stop whatever action occurs. Next determine the correct exposure for you're lighting. Action indoors should be photographed with a flash unit. The latter is by far the better light for stopping action, as flash will stop all movement. Dog and cat images should have a furry textured feeling.
Sunlight needs little explanation.
Flash is most important in taking action photographs, but it also has other useful functions. First, it produces the previously mentioned, eye and iris, for certain expressions. It is best to use multiple flash in such instances. Balance the lighting by using one flash on the camera, another as a slave unit. Flash is also excellent as a balance, fill-in, or supplementary light to sunlight either in or out of doors.