The main components are nitrogen or green materials, carbon or brown materials, bacteria found within existing compost, animal dung and soil, Water, oxygen, and the size of your heap also factor into the recipe.
Aerobic compost heaps need to be at least a metre cubed so the heap can insulate itself enough to retain the heat it generates. Adding insulation such as plastic or cardboard can help. The materials need to be available and on hand all at once. This isn't a problem for the local refuse centre, which uses this process to make massive amounts of compost but can be a challenge at home.
The main problem is usually coming up with enough of the right kinds of nitrogen or green-type materials to process the amount of carbon or brown materials most gardens generate through leaf fall, prunings and spent plants.
Plants such as banana (ornamental and fruiting), canna lily and taro are excellent to have on hand. Firstly all these plants are nitrogen-rich and secondly they hold significant amounts of water in their leaf and stem structure. As the plant decomposes, this reservoir releases moisture into the heap, fuelling the bacteria.
Most aerobic compost heaps I've read about seem to have a carbon to nitrogen ratio of one part nitrogen to three parts carbon. This is fine, but because I like to use the nitrogen materials I mentioned earlier, I use a 50:50 ratio.
Soft green materials such as lawn clippings decompose quickly but in large amounts can go mushy and smell so should be mixed thoroughly through a carbon material such as dried leaves before you put them into a heap.
Hedge clippings on the other hand can be very woody and may need to be broken up and mixed with softer material. Carbon usually needs to be broken up as much as possible - a machete is excellent for this. If a plant has flowered I treat it as carbon, as it has become sinew.
To start a compost bin, I use packing pallets to form a box then line the box with cardboard. I layer in the materials 200mm thick at a time with a bacteria or inoculator layer (either compost from another heap, soil or animal dung) in between each layer. The layers are even and the corners neatly packed.
After adding the bacterial layer to each layer of carbon I soak the heap for about a minute with a hose.
When it's a meter and a half high, I cover the heap with a tarp, for three weeks in summer and nine weeks in winter. I remove the contents then replace them. This aerates the compost and heats it up again. It also gives me the opportunity to check the heap. If it's too dry I add water. If it's too wet I add carbon. Depending on the air temperature I may repeat this process up to four times.