I know you have heard it, compost. What is more green than that right? I don't do this. I wish I did. My father has issues with it, even though he unconsciously does it with all the grass piles in our backyard. But we do have a bin provided by the city that takes our 'green waste' away for us. Very nice.
If you decide that composting is for you, here is the basic needs. Compost pile needs two things; carbon (newspaper, cardboard, straw) and nitrogen (lawn clippings, food waste, plants). Put a ratio of 5 carbon to 1 nitrogen. You can leave it for a year, or rotate every few weeks adding water to be done in about three months. For easier organizing, have different piles that you rotate.