As an introduction to Fungi, watch the Crash Course video, Fungi: Death Becomes Them.
As you learned in the video Fungi are heterotrophs that absorb their food, they're not animals, and they're not plants, and they reproduce both sexually and asexually. Fungi, along with bacteria found in soil are the primary decomposers of organic matter.
Fungi are multicellular organisms, with the exception of yeast. Read about the structure of fungi the Structure of Fungi page.
There are four types of fungi you should know about:
Primitive Fungi - are aquatic and have flagellated spores. Some of these fungi are decomposers, and some are parasites.
Sac Fungi - yeasts, some molds, morels and truffles are all sac fungi. These fungi form a reproductive sac or ascus.
Bread Molds - often found on spoiled food. They form zygospores during reproduction.
Club Fungi - have fruiting bodies that are club-shaped. This group includes mushrooms, puffballs and shelf fungi.