Dynamics and astrochemistry in the cosmos frequently, and sometimes strongly, feedback on one another. Therefore, the most predictive simulations of the cosmos should include coupled dynamics + chemistry. The technical details of this coupling are worth considering, in part, because maintaining the conservation of charge and atomic species in a dynamical model requires care, but also because simulating chemistry at every location in a large, multidimensional dynamical model is generally prohibitively expensive. Here, we review how to ensure conservation of species and charge in the most common hydrodynamical numerical methods, how chemistry commonly feeds back onto the dynamics, and present guidelines for how to minimize the cost of modeling coupled chemistry + dynamics.