The species of Geastrum are known colloquially as earthstars. Each mature fruitbody consists of a puffball-like spore sac atop a star-like base. Some species are easy to identify visually, others are not.
Before you started looking at microscopic details, some of the questions you'd ask when trying to identify a Geastrum are:
You'd also note colour, texture and size.
Geastrum sp. is listed in the following regions:
Canberra & Southern Tablelands | Southern Highlands | South Coast | Central West NSW | Loddon Mallee