Bayesian statistics has gained great momentum since the computational developments of the 1990s. Gradually, advances in Bayesian methodology and software have made Bayesian techniques much more accessible to applied statisticians and, in turn, have potentially transformed Bayesian education at the undergraduate level. This article provides an overview of the various options for implementing Bayesian computational methods motivated to achieve particular learning outcomes. For each computational method, we propose activities and exercises, and discuss each method's pedagogical advantages and disadvantages based on our experience in the classroom. The goal is to present guidance on the choice of computation for the instructors who are introducing Bayesian methods in their undergraduate statistics curriculum. Supplementary materials for this article are available online.