The basic ingredients for compost are "browns," "greens," air and water. Browns like fall leaves and woody materials are high in carbon, an essential energy source for microorganisms in the compost. Greens like grass clippings and fruit and vegetable trimmings are high in nitrogen, an essential nutrient for the decomposer organisms.
For fall leaves and small garden clippings (six inches or shorter), a simple pile covered in winter and kept a little moist in summer will break down in about a year. Larger woody materials and fruit and vegetable trimmings do require a little more effort to compost, but not much.
Soil organisms from compost continuously generate fertilizers for your plants so you don't have to. Bacteria, fungi, and other microscopic organisms dissolve minerals in tiny rocks, recycle nutrients in dead plants and animals and release these into the soil where roots can absorb them. Some bacteria even "fix" nitrogen from the air, making it available to plants. To ensure these little workers stay on task, avoid fast-acting fertilizers and pesticides, maintain proper moisture levels, and keep all soil covered with mulch or living plants.