One of the "greenest" things you can do besides growing your own food, is composting.
What is compost? Organic matter that has been decomposed and recycled as a fertilizer and soil amendment. Compost is a key ingredient in organic farming.
I try and live my life by the R's mantra: Refuse, Reduce, Reuse, Rot (Compost) and Recycle.
Organic material disposed of in landfills creates large quantities of methane, a major global-warming gas. U.S. landfills are “among the single greatest contributors of global methane emissions,” 
according to the Natural Resources Defense Council. According to the EPA, methane is 20 to 30 times more potent than CO2 as a greenhouse (global warming) gas on a molecule to molecule basis.
"The exercising of the human spirit can take many forms, and the simple act of cleaning up after oneself is one of them. The careless dumping of waste out into the world is a self-centered act of arrogance — or ignorance."
I started out small. Just some free wood pallets used to dump my grass clippings after mowing my 1/2 acre yard. It would fill up fast before summers end. I had the same problem with dead leaves in the fall.
You can't tell from the picture but the pile in the corner was as tall as me. Plus I bagged another 12 or so large plastic bags worth. I'm not a fan of throwing things away so I needed to expand. The next iteration looked like this.
Here there are 5 separate areas. Each is about 5'x5' by 4' tall (or 100 cubic feet). One area for cold composting. One for grass clippings. One for leaves. One for hot composting and one for storing finished compost.
Here's the finished storing area.
Originally I was mixing the right ratios and turning it with a pitchfork. 
But this is laborious and it never seemed to reach the right cooking temps. It turned to compost but it took a whole year to do it.
So I did some research and was about to make my own compost tumblers from free 55 gal plastic barrels but then I found (thanks to John at 
http://www.youtube.com/user/growingyourgreens )  the Joraform 270. This is made in Sweden (they take composting seriously). The inside will reach 160 degrees! It wasn't free but it was just what I wanted. It makes compost in weeks instead of months. It's insulated so you can compost during cold months. It spins easily for mixing. Has 2 chambers. Galvanized and painted steel panels. It's high enough to park my garden wagon underneath to dump out finished compost. It'll keep the flies and other hungry critters out of the pile. It holds 70 gallons.
 
A compost pile needs these ingredients. Carbon and nitrogen with a ratio of 75% and 25%
For carbon I use dead leaves, shredded paper from my bills, toilet and paper towel rolls, straw, wood chips, sawdust, etc.
For the nitrogen I use grass clippings, weeds, spent vegetable plants, food scraps, egg shells, coffee and coffee filters (I even go by Starbucks once a month and they'll give you for free, all the used coffee grounds for that day. It's their Grounds For Gardens program), pulp from my juicer, etc. 
“Compost is more than a fertilizer or a healing agent for the soil’s wounds. It is a symbol of continuing life . . . The compost heap is to the organic gardener what the typewriter is to the writer, what the shovel is to the laborer, and what the truck is to the truck driver.”
If you've ever bought a bag of organic compost from a nursery you know that it isn't cheap. I have 17 raised garden beds to fill and amend so this makes great economical sense too.
Why use compost at all? Why not just dirt?
BENEFITS OF COMPOST
ENRICHES SOIL
• Adds organic material
• Improves fertility and productivity
• Suppresses plant diseases
• Discourages insects
• Increases water retention
• Inoculates soil with
  beneficial microorganisms
• Reduces or eliminates fertilizer needs 
• Moderates soil temperature 
Compost also adds slow-release nutrients essential for plant growth, creates air spaces in soil, helps balance the soil pH, darkens the soil (thereby helping it absorb heat), and supports microbial populations that add life to the soil.
Here's a small list of what can be composted:
From the Kitchen
1. Coffee grounds and filters
2. Tea bags
3. Used paper napkins
4. Pizza boxes, ripped into smaller pieces
5. Paper bags, either ripped or balled up
6. The crumbs you sweep off of the counters and floors
7. Plain cooked pasta 
8. Plain cooked rice 
9. Stale bread 
10. Paper towel rolls 
11. Stale saltine crackers 
12. Stale cereal 
13. Used paper plates (as long as they don't have a waxy coating) 
14. Cellophane bags (be sure it's really Cellophane and not just clear plastic—there's a difference.) 
15. Nut shells (except for walnut shells, which can be toxic to plants)
16. Old herbs and spices 
17. Stale pretzels 
18. Pizza crusts
19. Cereal boxes (tear them into smaller pieces first) 
20. Wine corks 
21. Moldy cheese 
22. Melted ice cream 
23. Old jelly, jam, or preserves 
24. Stale beer and wine 
25. Paper egg cartons 
26. Toothpicks 
27. Bamboo skewers 
28. Paper cupcake or muffin cups 
From the Bathroom
29. Used facial tissues 
30. Hair from your hairbrush 
31. Toilet paper rolls 
32. Old loofahs 
33. Nail clippings 
34. Urine
35. 100% Cotton cotton balls 
36. Cotton swabs made from 100% cotton and cardboard (not plastic) sticks 
Personal Items
37. Cardboard tampon applicators 
38. Latex condoms 
From the Laundry Room
39. Dryer lint 
40. Old/stained cotton clothing—rip or cut it into smaller pieces 
41. Old wool clothing—rip or cut it into smaller pieces 
From the Office
42. Bills and other documents you've shredded 
43. Envelopes (minus the plastic window)
44. Pencil shavings 
45. Sticky notes 
46. Business cards (as long as they're not glossy) 
47. Receipts 
Around the House
48. Contents of your vacuum cleaner bag or canister
49. Newspapers (shredded or torn into smaller pieces) 
50. Subscription cards from magazines 
51. Leaves trimmed from houseplants 
52. Dead houseplants and their soil 
53. Flowers from floral arrangements 
54. Natural potpourri 
55. Used matches 
56. Ashes from the fireplace, barbecue grill, or outdoor fire pit 
Party and Holiday Supplies
57. Wrapping paper rolls 
58. Paper table cloths 
59. Crepe paper streamers
60. Latex balloons 
61. Raffia 
62. Excelsior 
63. Jack o' Lanterns 
64. Those hay bales you used as part of your outdoor fall decor 
65. Natural holiday wreaths 
66. Your Christmas tree. Chop it up with some pruners first (or use a wood chipper, if you have one...) 
67. Evergreen garlands 
Pet-Related
68. Fur from the dog or cat brush 
69. Droppings and bedding from your rabbit/gerbil/hamsters, etc. 
70. Newspaper/droppings from the bottom of the bird cage
71. Feathers 
72. Alfalfa hay or pellets (usually fed to rabbits) 
73. Rawhide dog chews 
74. Fish food 
75. Dry dog or cat food
*Although I don't eat meat at home, with this Joraform Composter, you can compost meat, dairy, butters and cooking oils too. 
http://www.joraform.com/en/products/composters/jorakompost-125-270-400.html
Believe it or not, your poo and your dogs poo can (and should be) composted. You wouldn't want to use this compost for growing food in however. I have started composting my dog's poo (a 60 lb Golden Retriever) but I'm not quite ready to do my own. 
Composting poo probably sounds gross to you but it shouldn't be. Educate yourself and read The Humanure Handbook by Joseph Jenkins for free online here: 
http://humanurehandbook.com/contents.html
It's about more than just humanure, it's about science!  Not a reader? Then watch this: It's the Pee and Poop show: 
http://www.youtube.com/watch?v=tdN_3x8VNCY
This year I also plan on doing Worm Composting, or Vermicomposting. The worms poo or "castings" are excellent for adding to your garden.
And you can make compost tea which plants love. 
What Is Compost Tea?
It's a liquid fertilizer and disease suppressor that is made by soaking small amounts of biologically-active compost in water, often with other ingredients such as kelp or molasses to feed the microorganisms, and then aerated over a period of one to two days. The "tea" is then sprayed using a typical hand-held sprayer either directly onto plants, the soil, or it is applied as a soil-drench (root dip) for seedlings.
More to come on compost tea later.