Both the simulation research and software communities have been interested in optimization via simulation (OvS), by which we mean maximizing or minimizing the expected value of some output of a stochastic simulation. Continuous-decision-variable OvS, and gradient estimation to support it, has been an active research area with significant advances. However, the decision variables in many operations research and management science simulations are more naturally discrete, even categorical. In this tutorial we describe some of the research directions and results available for discrete-decision-variable OvS, and provide some guidance for using the OvS heuristics that are built into simulation modeling software.