The mass of the Sun is easy to determine using Newton's form for Kepler's Third Law of Planetary Motion, i.e.,

P**2 = 4 x pi**2 x a**3 / G / (Mass of the Sun + Mass of the Planet)

Here, P is the orbital period of the planet, pi = 3.14, a is the semi-major axis of the planet's orbit and G is the gravitational constant. (The value for G depends upon the unit system one chooses to work in.) Using the Earth and noting that the Earth is only 1/330,000 of the mass of the Sun, we determine the mass of the Sun from

Mass of the Sun = 4 x pi**2 x (A.U.)**3 / (G x P**2)

To calculate the mass of the Sun we choose to work in c.g.s. units so that 1 A.U. = 1,490,000,000,000 cm, P = 31,000,000 seconds, pi = 3.14, and G = 0.0000000667. We find that the mass of the Sun is roughly 1.99 x 10**33 grams. Note that in centimeters-grams-seconds (c.g.s.), all lengths are measured in cm, all masses are measured in gm, and the time is measured in seconds. There are other unit-conventions, for example, meters-kilograms-seconds (m.k.s.) in which I measure lengths in meters, masses in kilograms, and time in seconds. It doesn't matter which unit system you choose as long as you are consistent.

The method used to determine the masses of stars is precisely the same method (or a variant of the method) used to determine the mass of the Sun. (Except that one uses double star systems rather than planetary systems.)

Information provided by: http://zebu.uoregon.edu