Photographing kids is all about treating them as equals - get down to their level, see the world from their point of view, match their energy level, and shoot lots and lots and lots of frames!!! This requires quite a bit of confidence in your camera skills, as this is not the time to ask for a "hold it while I focus/check my exposure/set my white balance/compose with the rule of thirds"... this is the time to get down, move fast, laugh out loud, and keep hitting that shutter button, counting on the skills you've honed with more static subjects (like grownups...)
One of my favorite tools to use with kids is a LensBaby - that's a very basic, all manual lens, that has been intentionally build without any correction for focus curvature, aberrations, etc, etc. It's simply the bottom of a ****e bottle, glued to the end of a short rubber hose - you grab it, push and pull on it till the key part of the image (the kid's eyes) look in focus, and hit the shutter!
It helps to have your camera set on 8 frames/second, and shoot a long burst, while gently letting go of the lens, to hopefully hit that sweet focus shot... Pulling the lens into the body of the camera is necessary to get it to focus (as the lens starts out far enough to focus on about 2 feet away), but if you pull too hard, you'll wind up focusing behind the subject!
Our modern auto-focus cameras have very bright screens, with very low contrast, which makes it pretty much impossible to critically judge manual focus - if you are truly obsessed (as I am), you'll find that you'll get a very, very low percentage of correctly focused images.
The lens has a manually changed aperture disk, as did lenses in the mid-19th century - but you'll quickly pick your best loved effect (from no aperture disk=F2.0, all the way to F16 - mine is usually F5.6), and then use either Aperture Priority, or just good old manual exposure (for those of us who remember how to use film....).
The lens has a very high level of flare, so you don't need to overexpose (as you normally do in digital, to insure sufficient shadow detail), but do shoot nothing but RAW! You'll later need to bring up the Black levels, play with curves to increase the contrast, and struggle with the white balance (as the flare can contaminate the color, as well). It helps if you're aiming for pleasing, warm color (though I have shot some jobs with it, too, where I've gone to great lengths to gobo the lens).
If you do want to use it for commercial shoots (or any shoot where you have complete control - that'd rule out any live child), buy the 3G model, which has 3 metal rods to lock down the lens position, and a very limited helical screw mount, to tweak the focus - it works much better for control and repeatability, but is way, way too slow for shooting live kids - stick with the 2G model, the simple hose.... I use both, as the situation demands, and can't say enough good things about them!