Making compost can be as simple as piling materials and letting them sit for a year or so. This is a good and time-honored way of making compost. In this work, this is called the passive method. At the opposite extreme, you can put together compost like a fine souffle, following a recipe to add just the right materials, managing it to get the interior heat to just the right level, and moving it through the decomposition process as rapidly as possible, in managed composting. You might also hear this method called hot composting.
Besides these two basic methods, you can let worms make your compost in vermicomposting; you can make compost without air, or anaerobically, or you can dig compost materials right into the soil where they rot on their own, in sheet composting.