Question

How could you use a microscope to help determine whether a specimen is a living or nonliving thing

Answer 1

Whether living or non living:
When you put a sample of tissue under a microscope, if u can see a cell membrane, and can identify some cell structures like nucleus, mitochondria, vacuoles etc. , it was living, if not, its a non living thing.

However some cells don't have a nucleus( eg. prokaryotic cells), but all cells have a cell membrane or some sort of protective covering to contain the cell's insides. 

To check if your specimen maybe-once living, maybe-still living "something", is living, get a look at it through an electron microscope - thats the best microscope ever- and see if the mitochondria's making any ATP( adenosine triphosphate, source of energy for most organisms), if it does, its living. If not, non living. :)