A lot of green waste can be generated from a productive vegetable garden. Composting it not only saves it from going into the land fill but also provides a great soil amendment that you can put back into your productive garden. You can work it in as you prepare for the next season's plantings or you can just apply it to the soil surface as a mulch. Directions to make compost in a hurry (pdf).
A few things to avoid composting include any animal manures, meat, bones, kitty litter, and plants with serious disease problems or weeds that either have heavy rhizomes or seed heads.