Hydrogen mobility upon and pathways into connected surfaces of a fcc metal, using the Ni (100), (110), and (111) faces as a model, are examined through computational methods. Our interest is in finding the time scale for an initial H-atom population density deposited on the surface to reach an equilibrium surface and sublayer distribution, and to understand the H dynamics in the region of Ni surface steps. The activation energies for H mobility from site-to-site are determined using a realistic potential energy function, and a set of 232 transition state theory rate constants governs the H-hopping model. A handful of the TST rate constants are compared favorably to very accurate calculations of rate constants for the same potential using a 3-d quantum mean field method. The set of TST rate constants are used in a kinetic Monte Carlo solution of the rate equations for surface hopping and surface penetration to complete the picture. We find that fast diffusion of H atoms occurs on all of the Ni surfaces with H atoms rapidly exchanging surfaces via both concave and convex step edges, and leaving the less stable (111) face. We examine the time scale for the approach to equilibrium for the H atoms on both the surfaces and sublayers. The effect of convex step edges vs the effect of direct terrace penetration for the H atoms is examined, and we find that at temperatures below about 1000 K the H-atom penetration at convex step edges becomes the favored pathway to the subsurface. As the H atoms flow via the step edges to the sublayer, a transient cycling current of H-atom probability is set up near the step edge, which fades away as equilibrium is reached.