Careful control of the microstructure of an adsorbed monolayer of colloidal particles is important for creating nanostructured devices through self-assembly processes. We present a computational model study for self-assembly of colloidal or nanoscale particulate systems. We develop a new technique for simulating colloidal adsorption processes, and we examine the kinetics and the structure formation on the surface. The technique allows the simulation of a nonhomogeneous suspension with an open boundary that is in equilibrium with a bulk suspension of known volume fraction, including the mean-field forces from the bulk solution and particle flux between the simulation box and the bulk. Short-time kinetics follow a power law similar to the case of diffusion-limited adsorption. Long-time kinetics fit a 2/3-power law form [P. Schaaf, A. Johner, and J. Talbot, Phys. Rev. Lett. 66, 1603 (1991)] and kinetic coefficients are calculated. The zeta potential of the particles is the dominant parameter controlling the final surface coverage, but the zeta potential of the adsorbing surface is the dominant control for the ordering of the adsorbed system. Particles with larger Debye layers (lower salt concentrations) order more easily. Jamming limit coverages are compared to existing equivalent hard-disk models and an energetic model. Since the process is kinetically frustrated, particle exclusion effects play a major role in determining coverage as well as structure.