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The basic mechanisms responsible for producing winds from cool, late-type stars are still largely unknown. We take inspiration from recent progress in understanding solar wind acceleration to develop a physically motivated model of the time-steady mass loss rates of cool main-sequence stars and evolved giants. This model follows the energy flux of magnetohydrodynamic turbulence from a subsurface convection zone to its eventual dissipation and escape through open magnetic flux tubes. We show how Alfven waves and turbulence can produce winds in either a hot corona or a cool extended chromosphere, and we specify the conditions that determine whether or not coronal heating occurs. These models do not utilize arbitrary normalization factors, but instead predict the mass loss rate directly from a star's fundamental properties. We take account of stellar magnetic activity by extending standard age-activity-rotation indicators to include the evolution of the filling factor of strong photospheric magnetic fields. We compared the predicted mass loss rates with observed values for 47 stars and found significantly better agreement than was obtained from the popular scaling laws of Reimers, Schroeder, and Cuntz. The algorithm used to compute cool-star mass loss rates is provided as a self-contained and efficient IDL computer code. We anticipate that the results from this kind of model can be incorporated straightforwardly into stellar evolution calculations and population synthesis techniques.