Add fresh or air-dried herbivore dung and cover the dish with its glass lid. Put it in a cool room and keep the towel moist but not wet. Every other day, examine your crop with a magnifying glass or, better still, one of PSMS's dissecting microscopes. If you want to identify your fungi, you'll need a compound microscope and some arcane literature , both of which are available from the PSMS library. There seems to be a typical progression of fungi in these tiny fungus gardens.
Molds appear first, followed by zygomycetes that fling sticky spore capsules at the glass lid.
Finally you may see an exquisite Coprinus with a minute cap that appears to be encrusted with diamond chips. Deer, elk, and rabbit dropping are easy to find and culture. Many fungi are particular about the kind of dung they will grow on, so to see a variety of fungus species, select dung from a variety of animal species. I suspect that dung from different places will produce a greater variety of fungi. Elephant dung from Thailand will likely produce fungi quite different from the fungi produced on elephant dung from Seattle.