The key starts out by asking whether your moss has some exceptional and immediately obvious traits. First off are the peat mosses (Sphagnum) and the family Polytrichaceae.
 

The large and difficult genus Sphagnum is distinctive microscopically. Sphagnum leaves are composed of two types of cells: narrow green (photosynthetic) ones that form a mesh-like network surrounding much larger thin-walled non-living cells. The large dead cells have pores that enable the cells to become filled with water. Sphagnum peat is an effective soil ammendment that increases water-holding capacity.

Sphagnum palustre whole plant

Sphagnum sp. cells

Another group that is distinctive morphologically is the family Polytrichaceae, which includes several widespread and robust mosses. The Ohio haircap moss, Polytrichum ohioense is common on the ground in woods throughout the state.

Most moss leaves are one cell thick. But Polytrichum leaves are several cell layers thick, and much of upper surface is covered by ribbon-like sheets of stacked cells running lengthwise, called "lamellae." Details of the lamellae are used to distinguish some species: for example P. commune has terminal cells of the lamellae notched, whereas the gametophytically very similar P. ohioense has those cells flat-topped or slightly bulging.