Besides kitchen scraps, one can recycle many other things such as shredded cardboard and paper bags (without ink) or lint from the dryer. Some things can be burned and ashes added to the pile.
After my kitchen bucket is full, I pour it out into one of the milk crates I keep in my back yard. Over these I add a layer of soil (the microorganisms inside do most the work of decomposing) and then a layer of leaves. If possible, chop or crumble the leaves before adding. Also look for local worm castings to add, but it may not be long until worms find their way to the pile and do the work for you. If not, you may find them in various places such as under rocks. Just carefully pick them up and add them to your pile.
This process is repeated each time I have another bucket of scraps and until the crate is full. Then I move on to another crate. After awhile, the items in the first crates will shrink, so more layers of material may be added. Just try to keep in order which you did first or which crates are the oldest. It's easy to tell by looking at them.
When you run out of crates to use, simply go to the first couple of them and empty them into a pile in an area that gets a reasonable amount of sun. The sun aids decomposition, but you don't want the piles to get overly dry either. If that happens, simply add water.
Now and then, turn the pile on the ground with a pitchfork or whatever implement is available. You should see steam come out on a cool morning (or the fact that the pile is shrinking, rapidly). This is a very good sign that the pile is "cooking" properly. Continue to turn the pile from time to time. Another sign of good composting is there is no bad smell. It should have an earthy smell that no nature lover can resist. Plus you may see seeds sprouting out of your pile. I've had both cantaloupes as well as avocado seeds sprout forth in different piles, the former producing whole fruits. (Later note: One year I tossed several rotten tomatoes and had a large quantity of tomato plants growing which I transplanted and they produced a good amount of fruit!)
When the pile gets large enough, make another one nearby. Do not empty any more crates into the first. You want it to completely decompose or turn into useable compost. Compost that is not decomposed properly can "burn" plants by the heating property is possesses described above, unless you are strictly using it as a soil amendment and not for plant food.
Good soil can be created by adding plenty of finished compost over time, and many problems with the soils balance will gradually become corrected. There is a saying, "The first year your garden sleeps, the second it creeps, the third it leaps." That's because of increasingly healthy soil.
Feed plants with a layer of finished compost. Watering will allow nutrients to wash down into the soil beneath.
Have fun and remember to, "Compost- because a rind is a terrible thing to waste!"
UPDATE ON 3/2014: We moved to the country, and I no longer have my little milk crates. I graduated to nailing together four wooden pallets. The resultant compost container is roomy, airy and easily moveable whenever I need to start a new pile!