We investigate the most basic situation of heterogeneous crystallization: crystallization of hard-sphere colloids in the presence of a flat hard wall. Using a combination of confocal microscopy and nonequilibrium Brownian dynamics simulations, microscopic time-resolved information is obtained on an individual-particle level. Initially, particles near the wall rearrange before an extended regime of crystal growth is found. During growth, we can directly observe a depletion zone in the fluid next to the progressing crystal-fluid interface due to the single-particle information provided by microscopy and simulations. This also allows us to follow the relaxation of the crystal layers and the progression of the crystal-fluid interface. In good agreement between our experiments and simulations, as well as previous studies, the growth rate shows a maximum in its dependence on the bulk volume fraction.