We use three-dimensional simulations to study the atmospheric circulation on the first Earth-sized exoplanet discovered in the habitable zone of an M star. We treat Gliese 581g as a scaled-up version of Earth and examine the long-term, global temperature and wind maps near the surface of the exoplanet --- the climate. The specific locations for habitability on Gliese 581g depend on whether the exoplanet is tidally-locked and how fast radiative cooling occurs on a global scale. Independent of whether the existence of Gliese 581g is confirmed, our study anticipates the use of meteorological solvers to quantify the atmospheric circulation on potentially habitable, Earth-sized exoplanets, which will be the prime targets of exoplanet discovery and characterization campaigns in the next decade.