1. When photographing faces, get close. I know it seems obvious. But when I want the face, I want the FACE. Especially with kids. Grown ups tend to shake, giggle, or threaten physical harm when you get too close. But with kids, start out as close as you feel comfortable.
Then, GET CLOSER. Bring the camera to the point where you feel uncomfortable. Then move in another inch. Yes, that is what I said. This is where a zoom lens comes in handy, as you can get close without being annoying.
2. Lose the background. In photographing people, I prefer the background to be blurry. It keeps the focus on the face. If you have a fancy camera like a DSLR (Digital Single Lens Reflex), you can control some of that depending on the size of the aperture. But if you are lazy or don’t have a fancy camera, fill the frame with face and person so the background is unnoticeable.
Provoking your subject with potty humor works sometimes too. In fact, I highly encourage it.