Step 1: What You DON"T Need
So, I'm going against the flow, not letting the man keep my head down, fighting the power, etc...
And thus, in direct contradiction to the name of this step, here is what you will need:
1) A 10 gallon plastic bucket, like the kind 3" chlorine tablets are sold in.
(If you are going to use this bucket, wash it out first. Chlorine kills living things - look it up)
2) Some starter soil. Just grab a shovel, and dig some up. Any kind will do.
3) A shovel, or some other scooping/scraping/turning device. Actually, use a shovel, because I managed to wound myself with my rusty rebar and had to get a tetanus shot. It hurt. A lot. Trust me.
4) Water. The essence of life.
5) Compost material. Leafy yard clippings, plant-based kitchen scraps, paper, eggshells, whatever.
6) Patience, patience, patience. And for those of us with problems waiting, a computer/book/family pet for your amusement,
Step 2: A Necessary Part of Every Good Instructable Is...
The author, sole proprietor, and cynical bastard that wrote this -ible (recon506) hereby absolves himself of any responsibility (thus screwing you over) towards you, in respect to damages to life, limb, property, beloved family pet, hated sibling, your bank account, etc, etc, etc...
*I do not take credit for this flash video. I don't know who do give credit to. I just find it appropriate,
Step 3: Down to the Good Stuff
Then go get yourself another half bucket-full of dirt from your yard. (I assume you have one)
Grass clippings are a good idea to start with if your grass is lush, soft, and a deep-green color. All other types of grass are either not juicy enough, or their cell walls are too hard for them to break down easily.
Step 4: Cake Time!
This is not the kind of cake you will want to eat. This cake is only delicious to worms or the bacteria that are going to make your compost for you.
1) Spread an inch thick layer of dirt covering the bottom of your bucket
2) Spread an inch thick layer of clippings over that.
3) Repeat steps 1-2 until your bucket has only 2 inches left from the top, or you run out of clippings/dirt.
4) Top it all of with a half-inch layer of dirt on top, to lock the moisture and heat inside when it starts to ferment.
Step 5: It's a Waiting Game
There is still some manual labor involved from now on until the composting process is over.
Every week, you should check the moisture level of your compost bucket. The composting mixture should be uniformly like a wrung-out sponge. Too much water and you will drown your bacteria. Too little water and your bacteria will become little mummies.
Skipping a week or two isn't fatal (usually), but you can always remedy the situation by adding more water and sprinkling in some potting soil, courtesy of your neighborhood hardware store.
Furthermore, every week, after checking the moisture level, you should firmly close the bucket with the lid that came with it, tilt it on its side and roll it for about 4 full revolutions back and forth a couple of times. This loosens and counteracts the compacting action that may have occurred during the week. It also introduces oxygen into the compost, making the little critters (bacteria) happy. Next, tilt the bucket so it is standing right-side-up and spin it head over tail for about 5 revolutions. This makes the bottom soil rise and the top soil sink.
Step 6: The Science...
Occam's Razor is a doctrine that states that the simplest solution is usually the right/best one.
Composting occurs when naturally-occurring bacteria in the soil (hence the soil I told you to put in) break up the organic matter, relying on oxygen and water as their fuel source. This breaking up of the organic matter releases the nitrates that the plants use to create amino acids, and puts it back into the soil (that I told you to put in) increasing the volume and nutritional value greatly.
Thus, now instead of having to waste time and energy converting potassium nitrite into other forms of nitrogen, the plants have a ready-made source at their finger-tips (root-tips if you will).
Basically - Occam's Razor in a nutshell.
There needs to be a balance between moisture and oxygen in your compost pile/heap/bucket. It's not an exact science, but trial and error will help you along towards being a compost master. You can tell if the bacteria are aerobic (active) as opposed to anaerobic (inactive) by the rotting-garbagey smell that accompanies the latter.
A 10 gallon bucket's worth of compost will take about 4 months to complete, and that is during an Arizona summer, with the average temp well over a 100 degrees Fahrenheit. I actually skipped the last two months of watering and turning my pile, but at that point it was self-sustaining. I have no explanation for it as of yet, but I'll try to figure it out and I will update this -ible when I do.
UPDATE: I have had a comment (kudos to GroovyGuru) about the time it takes to fully compost a certain amount of material. I am sorry if I was misleading in the above paragraph - most sizes of containers will in fact be completed in about 4 months. This is due to the fact that the increased volume allows for more bacteria to be present in the mixture, thus meaning that the bacteria to waste ratio will be almost the same for any amount of compost that you wish to create.