For those who haven't used it, the typical usage is to use Stan in combination with other languages (most commonly R). In the Stan language you define a model, specifying the data you'll get, potentially transformations to that data, then a set of parameters you want to fit, then finally a model saying how those parameters interact with each other and the data. You can also define priors for parameters. Then typically you save that model, and using R pass in the variables to a Stan call. The resulting fit object is returned to your original environment automatically.
It actually fits the work style reasonably well. All data munging happens as before, but instead of having some complicated model expression in, say, a glm() call, you have it in Stan language.
If you're interested in this, Gelman has two great books. Gelman & Hill's Hierarchical Models[2] which is applied and geared towards social science researchers, and Bayesian Data Analysis[3].