Compost is organic material which has undergone decomposition by microorganisms and is used as a soil amendment.
Composting is normally thought of putting a pile of organic matter in a pile to allow it to break down with either bacteria, or fungi often taking a year or more, but sometimes taking as few as 3 weeks.
Bacterial dominated composting: the most common method of composting performed by adding bacteria to rotting organic matter
Fungal composting: the second most common method for composting adding different types of fungi to a compost pile in order for it to break down while feeding your other plants in the garden with Endomycorrhizal fungi, and Ectomycorrhizal fungi when adding it to the soil in a symbiotic relationship. In order to keep a healthy ammount of these two types of fungi you need to ensure the fungi has enough soil to eat and add more as needed.
Insect composting: to have food is done by taking your compost, and dumping it somewhere random in your field for the insects to go after as they prefer decaying material.
The composting process can be accelerated by monitoring and managing the feedstock, the size and temperature of the pile, air and water infiltration into the pile, and various other factors. The temperature of the pile is primarily driven by the carbon to nitrogen ratio of the constituents. Other methods include sheet and trench composting.
Finished compost is useful as a fertilizer, soil amendment, and for erosion control. You can add finishing compost directly to the soil any time along the way.