Any equations or research paper would be helpful.
Reflection spectroscopy in visible and IR wavelengths (using sunlight reflected from asteroids and collected by ground- and space-based instruments) allows for chemical and mineralogical characterization. See an intro here, with links to other sources of background info:
Other in situ spectroscopic methods (e.g., Raman) can be employed by spacecraft or surface systems which can actually touch an asteroid.
All of the above spectroscopic techniques can be employed on asteroidal samples returned to labs on Earth by sample-return spacecraft. See more on this at this Stack Exchange answer to a question about the OSIRIS-REx mission:
There are other characterization methods, but spectroscopy is a great way to start.