Composting is essential! There are different ways to accomplish this. For kids, I recommend two methods: Aerobic (with oxygen) and Vermi (worm) composting. It is quite simple to do this, but it does take a commitment and requires extra work. In my way of thinking, it is absolutely worth it. The more effort that you put into it, the more compost you can get out of it.
Aerobic composting is the "decomposition of organic matter using microorganisms that require oxygen. The microbes responsible for composting are naturally occurring and live in the moisture surrounding organic matter." (From globalcomposting.solutions) This is best done in a compost bin, which there are many options. A single bin is the simplest, but not the easiest. A double bin enable one side to be left alone to decompose, while the other side is filled with organic matter (i.e. food scraps). If you are ambitious and have the space, building a three-section compost bin will allow for more organic matter to be processed. There are many different "recipes" for what goes into a compost bin, but the easiest way to guide this is to add and mix together equal amounts of "green" and "brown" ingredients. Green materials are nitrogen-rich and usually wet (food scraps, grass clippings, and weeds, for example), whereas Brown materials are carbon-rich and usually dry (small branches and dry leaves, for example). More information can be accessed with the button and link above.
Another composting system is Vermi or worm composting. This is fun if you like worms or have little space. I know some people who even do this inside their houses. I love worms! They are so interesting and helpful to our environment. The kind of worms that are used in vermi composting are Red Worms or Red Wigglers, not Earthworms that can more commonly be found when digging in the soil. More information about worms can be accessed with the button and link above. There is a great song for kids called "Lots of Worms" on the "Songs with audio" page on this website.