Nearly any organic material will compost, but for quick fertilizer production you should choose only the best materials. Compost a mixture of high-cellulose and high-nitrogen debris. Avoid things that come in big chunks--wood breaks down slowly, but wood sawdust in reasonable amounts composts well. Pay attention to the size and environment of the pile. Consider the compost heap a living thing that responds to water, shelter and food. Treat it well and you'll have finished compost in weeks, not months.
Locate the compost heap on well-drained ground in partial shade. Plan for a heap about 5 feet in diameter and 4 feet high, since the pile must have enough mass to generate and maintain its own heat. The National Resources Conservation Service recommends starting with at least a full cubic yard of raw materials.
Build the compost pile with a balanced mixture of high-cellulose and high-nitrogen materials. Alternate layers of fallen tree leaves, sawdust or shredded newspaper with layers of green grass clippings or livestock manure. Exact proportions aren't critical but try to make the pile 2/3 cellulose and 1/3 high-nitrogen wastes, by volume.
Use a shovelful of good garden soil or yard soil to inoculate the pile. Compost starter makes an expensive alternative to the cheap supply of beneficial microbes in ordinary dirt. Scatter soil lightly over every third layer of the new compost pile.
Water the pile thoroughly. Two or three gallons of water sprinkled evenly over the pile should soak in well enough that squeezing a handful of debris yields a few drops of runoff.
Cover the cone-shaped pile with a tarp wrapped around it tepee-style with the overlapping edges forming a vent at the top. The shape aerates the pile while protecting it from rain and wind. Weigh down the edges with stones or bricks.
Check the pile for heat after a few days. An active pile produces heat and steam, and in cool weather vents a stream of vapor out the top. As the pile exhales water vapor, add more water to keep the process going.
Break the pile down with the pitchfork in two or three weeks. Mix the layers thoroughly and turn the debris formerly at the surface of the pile into the inner core. Add enough water to keep all parts of the pile damp.
Repeat the cycle until the compost heap no longer heats up when turned. Use a shovelful of the finished compost as starter for a new heap.