Special computational techniques are required to compute absolute crystal nucleation rates of colloidal suspensions. Using crystal nucleation of hard-sphere colloids as an example, we describe in some detail the novel computational tools that are needed to perform such calculations. In particular, we focus on the definition of appropriate order parameters that distinguish liquid from crystal, and on techniques to compute the kinetic prefactor that enters in the expression for the nucleation rate. In addition, we discuss the relation between simulation results and theoretical predictions based on classical nucleation theory