In ?, we introduced a unified hierarchical Bayesian semiparametric model for genetic association studies of quantitative traits in the presence of population stratification. The model uses a Dirichlet Process Mixture (DPM) construction to account for stratification in making association inference. It also involves a nonparametric sparsity prior to accommodate the expectation that most genetic markers are unrelated to the phenotype in a large association screen. In this technical report, we describe the necessary computational details for implementing the DPM model (C code available from http://www.biostat.mcw.edu/software/SoftMenu.html). We begin with a short description of the DPM model, and then discuss its implementation through Markov chain Monte Carlo (MCMC) sampling.