How are steller masses determined?

Answer 1

We can calculate the masses of the sun and some binary stars, if we can measure the distance and period of orbits around them. This follows directly from Newton's theory of gravity. The masses of other stars can be inferred from their spectral class and stellar theory. We expect, for example, that any G2V star will have a mass and luminosity similar to the sun.

Answer 2

Stellar masses can be accurately determined for eclipsing binary stars. Given the photometry of the eclipse, the velocity of the stars in their orbits, and the period of the orbit everything about the orbits and the masses of the stars can be calculated. Other, non-binary stars can have their masses estimated by careful spectroscopic comparison with the eclipsing binary stars.