Almost all digital cameras have a shutter-priority exposure mode these days and it's a great tool if you occasionally (or frequently) shoot action subjects. (And, by the way, if you have three-year-old living in the house, that qualifies as a action subject.) As long as you have a decent amount of light this mode will almost always assure that you get sharp action photos.
The shutter-priority mode is a fully automatic exposure mode and it sets both shutter speed and aperture for you, but it gives priority to selecting the fastest shutter speed available. By setting this mode you're telling the camera that what's most important to you is freezing the action and that depth of field (near-to-far sharpness) is a secondary consideration.
You can also increase your odds of getting good action-stopping photos if you time your shots for the peak of action. To capture this shot of a teenager on a bungee ride at a carnival, for example, I watched him bounce and turn head-over-heels a few times and then, when I thought he'd reached the peak of his jumps, I shot. I worked out a pretty good timing sequence by watching him and was able to get quite a number of sharp photos of him.