Let me tell you why I compost.
First, I hate taking out the trash. I used to trade my sister for any other chore, even cleaning the bathroom, just to avoid the garbage cans in the alley. I'd much rather take a pretty bucket of kitchen scraps out through my garden to the compost pile. More compost means less smelly garbage!
Second, I'm cheap. Why pay for compost for my garden when I can make my own? Now, granted, I still buy compost. Our soil started out pretty awful, and I haven't been composting long enough to make up for it yet. But I'm getting there quickly with all the manure our chickens added this year!
Third, I just really like the whole cycle of life aspect. If I can return our food scraps to the soil and enhance it, why would I have them trucked to the landfill instead? Or give our leaves and grass clippings away to the city so they can make compost and sell it back to me? There I am being cheap again.
I'll let Wiki explain how to compost. He does it much better than I could. Also, check out this great slideshow which shows just what to do so simply your kids will want to take over the job!