How would I identify the type of paper being used in a folded origami?
You pretty much can't, unless it's specifically listed in the description of the piece.  The sheer variety of papers used worldwide, and the fact that some creators, like Michael LaFosse, make their own paper specifically for the model they're folding, means that your chances of accurately identifying the paper used is going to be very very tough, especially if you can't judge the thickness, sizing, or the fiber content by touch.

That said, the appearance of some papers is very characteristic, and if you have experience with kami, elephant hide, Canson watercolor paper, various craft papers, tissue foil, etc., some of those may be self-evident. Every origami folder tends to be intimately familiar with kami (so-called "origami paper") and can usually identify it on sight both from appearance and usage.

Characteristics of the paper that might lead to identification would be the surface texture being shiny or matte (surface sizing), fiber appearance/color, thickness/weight, and, of course, the size.