Vapor deposition simulation programs have been developed using Monte Carlo methods to determine the molecular dynamics of condensation, evaporation, and migration on the lattice. The simulation methods employed in the programs are developed in detail. The principle application will be to systems that permit a comparison with Honig's work, although the simulation methods are easily applied to a variety of other problems. The results of the simulations demonstrate that Honig's treatment is quite accurate and is a substantial improvement over previous treatments. This agreement also serves to build confidence in the use of Monte Carlo methods in simulating molecular dynamics for vapor deposition studies.