We study the morphological equilibration of a finite, facetted crystal by use of phenomenological equations of motion. The relevant atomistic kinetic processes (edge transfer, kink attachment and/or detachment, terrace hopping, and surface diffusion) are introduced progressively with special attention given to a proper treatment of the latter. Unlike all previous work, the role of individual step motion (including the effect of step-step interactions) is considered in detail. Approximate analytic results are obtained for two- and three-dimensional model crystals and compared to the work of others. Numerical results for the time dependence of the equilibration and the shape of the crystal during equilibration are presented for a model two-dimensional crystal in various limits of the kinetic parameters. Characteristic behavior is found when the different kinetic processes are individually rate limiting. Although each facet remains flat on macroscopic scales, multiple-step generation is found to lead to interesting microscopic step distributions and equilibration scenarios. The latter might be observable by appropriate microscopies.