What are the best micro organisms to break down compost?

Worms of any kind are very useful in making compost, as they eat and process dead plant material in the heap, but they aren't micro-organisms. There are billions of micro-organisms in every spadeful of soil, ie bacteria which break down organic matter into its basic chemical constituents. A pile of plant material will in time rot down to compost even if there are no worms in it, though the process will be faster if some redworms are present. You also need moisture and oxygen to start the process, whcih will generate heat and this really gets things going. Consequently you need to turn your compost heap every few weeks, to fluff it up and let in more oxygen, especially in the warmer months when the compost is capable of heating up properly and rotting down fast.