Kingdom Fungi

The fungi are eukaryotic, multi-cellular heterotrophs; their cells possess walls, mostly of chitin, although the chains of cells (termed hyphae) are frequently not completely separated from each other by a wall. Classification of fungi is based primarily upon their means of sexual reproduction. Hyphae should be visible in almost any slide. 

Phylum Zygomycota
These are often called bread molds, and such species are common and typical. These fungi are identified by being haploid without motility in any stage. An example is:
Rhizopus
This is a black bread mold; all molds found on bread are not necessarily this. The dark, spiky zygosporangium found between two suspensors is diagnostic; stalked sporangia, which produce spores, are usually also visible. 
Phylum Ascomycota
Although most species in this group are rather small, some fairly large forms look more or less mushroom-like. The distinguishing feature is that they reproduce by spores produced in an ascus, which is typically a tube- or vase-like structure containing eight ascospores. Examples are:
Penicillium
This is the type of fungus that produces penicillin; frequently found on spoiled fruit. Branching conidiophores are a distinguishing feature.
Peziza
This group represents one of the more mushroom-like ascomycotans. There are lots of species in this genus, most resembling a saucer with upturned edges; the asci are usually on the upper (inner) spore-producing surface (S). Hyphae (H), and asci (A) with eight ascospores  (8) are easily seen.

Phylum Basidiomycota

Most of the species that you would think of as mushrooms or mushroom-like organisms belong to this group. Spores produced on a basidium, a microscopic fist-shaped structure located on the reproductive surface of the fruiting body, are diagnostic. Examples are:
Puccinia
This is a rust that infects wheat. It has a complex life cycle involving several recognizable stages/forms, and a secondary host, barberry. We will see the aecia stage on a barberry leaf; it is haploid.
Coprinus
Named for its habit of occurring on dung, some species are delicious. This is a rather typical mushroom, except that species of this group self-digest soon after the spores ripen. It is a gilled mushroom, and the basidia occur on the gills (G), located on the underside of the cap of the fruiting body or basidiocarp (C). On high power, the basidia (B) and basidiospores (S) are easily seen.
Lichens
We will consider the lichens within the kIngdom Fungi. Of course, they are not just fungi, but a symbiotic pair of a fungus and some type of algae or cyanobacteria (green algae and cyanobacteria are most common). The fact that they are often as large as most macroscopic fungi, and frequently abundant in certain ecosystems, makes having a way to classify them more useful than, e.g., the ecologically similar, but microscopic symbiotic micorrhizae. When identified, the fungal component is more likely to be an ascomycotan, although basidiomycotans also form lichens. An example is:
lichen
The symbiosis is fairly obvious as the algal cells (A) are easily seen enmeshed in the fungal hyphae (H); you can also see where the lichen was attached to the substrate (D).  At lower power, the general structure is more apparent.