How many times have your kids done something so adorable that you couldn't wait to tell your spouse, but you can't remember it the next day? How many times did you want to capture it for posterity? How many times did you actually get a usable photo or video? You can't scrapbook it without some source material to start with.
Start at the Very Beginning
Take a look at your camera. Do you know what all the buttons, click wheels and dials are for? How about just half of them? If you don't know how those settings work, you're doing yourself a disservice. Sure point-and-shoot cameras are great for snapping a few pictures, but they're often capable of much more. Find an hour or two to yourself (easier said, than done, we know) and read through your camera's manual or check out a tutorial on camera settings. Get comfortable with what your camera is capable of, when to use each setting and crank your image quality all the way up in your settings. You can always get a bigger memory card (or keep spares in your camera case) but you only get one chance to capture that perfect moment.
Find the Right Angles
Once you know how to use your camera to your best advantage, it behooves you to learn a little about composition. Photofocus.com has a great piece on composition tips but the idea is that you use the angle and frame to emphasize the subject of the photo. Shooting from below can make a subject more powerful while shooting from above makes a subject less intimidating. The right angle and composition can make for some pretty funny pictures — think about what's funnier: a messy kid or a messy kid in the midst of the disaster he just created? So, say your child is dressed up as a superhero. Would you take a snapshot of them in the middle of the frame, looking at the camera and shot from your point of view? Or, might you get down low and shoot upward, with the cape blowing in the wind and looking into the distance as if staring down a villain? It depends on what you're trying to capture. If you're looking to document a costume you made the choice would be different than if you were trying to capture a mood or moment.