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 Msun and a radius of 0.57 Rsun. HATS-6b has a period of P = 3.3253 d, mass of Mp=0.32 Mjup, radius of Rp=1.00 Rjup, and zero-albedo equilibrium temperature of Teq=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 Teq < 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 Msun, 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 ~0.6 Msun star to ~7% and ~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.
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