An atomistic lattice-gas model is developed which successfully describes all key features of the complex mounded morphologies which develop during deposition of Ag films on Ag(111) surfaces. We focus on this homoepitaxial thin film growth process below 200 K. The unstable multilayer growth mode derives from the presence of a large Ehrlich-Schwoebel step-edge barrier, for which we characterize both the step-orientation dependence and the magnitude. Step-dynamics modeling is applied to further characterize and elucidate the evolution of the vertical profiles of these wedding-cake-like mounds. Suitable coarse-graining of these step-dynamics equations leads to instructive continuum formulations for mound evolution.