The mushroom or other sort of fungus that you see, is actually only the “flower,” that is, the reproductive part of fungus. The larger part of the fungus is a usually unseen network of thread-like filaments called mycelia that permeate and feed upon the dead material thus breaking it down. At some point, they come together to form the reproductive part that sheds spores, which germinate to form more mycelia. (See the text and please post questions.) Type into your browser: fungus mycelium photomicrographs
See also a time lapse video of mycelium growth:
A video of special interest, here is a TED talk describing the importance of mycelia in nature and perhaps in solving some of the world’s crucial problems.