Parameter estimation in evidence-accumulation models of choice response times is demanding of both the data and the user. We outline how to fit evidence-accumulation models using the flexible, open-source, R-based Dynamic Models of Choice (DMC) software. DMC provides a hands-on introduction to the Bayesian implementation of two popular evidence-accumulation models: the diffusion decision model (DDM) and the linear ballistic accumulator (LBA). It enables individual and hierarchical estimation, as well as assessment of the quality of a model’s parameter estimates and descriptive accuracy. First, we introduce the basic concepts of Bayesian parameter estimation, guiding the reader through a simple DDM analysis. We then illustrate the challenges of fitting evidence-accumulation models using a set of LBA analyses. We emphasize best practices in modeling and discuss the importance of parameter- and model-recovery simulations, exploring the strengths and weaknesses of models in different experimental designs and parameter regions. We also demonstrate how DMC can be used to model complex cognitive processes, using as an example a race model of the stop-signal paradigm, which is used to measure inhibitory ability. We illustrate the flexibility of DMC by extending this model to account for mixtures of cognitive processes resulting from attention failures. We then guide the reader through the practical details of a Bayesian hierarchical analysis, from specifying priors to obtaining posterior distributions that encapsulate what has been learned from the data. Finally, we illustrate how the Bayesian approach leads to a quantitatively cumulative science, showing how to use posterior distributions to specify priors that can be used to inform the analysis of future experiments.