We report the discovery by the HATSouth survey of HATS-6b, an extrasolar planet transiting a V = 15.2 mag, i = 13.7 mag M1V star with a mass of 0.57 M-circle dot and a radius of 0.57 R-circle dot HATS-6b has a period of P = 3.3253 d, mass of M-p = 0.32 M-J, radius of R-p = 1.00 R-J, and zero-albedo equilibrium temperature of T-eq = 712.8 +/- 5.1 K. HATS-6 is one of the lowest mass stars known to host a close-in gas giant planet, and its transits are among the deepest of any known transiting planet system. We discuss the follow-up opportunities afforded by this system, noting that despite the faintness of the host star, it is expected to have the highest K-band S/N transmission spectrum among known gas giant planets with T-eq < 750 K. In order to characterize the star we present a new set of empirical relations between the density, radius, mass, bolometric magnitude, and V-, J-, H-and K-band bolometric corrections for main sequence stars with M < 0.80 M-circle dot, or spectral types later than K5. These relations are calibrated using eclipsing binary components as well as members of resolved binary systems. We account for intrinsic scatter in the relations in a self-consistent manner. We show that from the transit-based stellar density alone it is possible to measure the mass and radius of a similar to 0.6 M-circle dot star to similar to 7 and similar to 2% precision, respectively. Incorporating additional information, such as the V - K color, or an absolute magnitude, allows the precision to be improved by up to a factor of two.