Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction events. Since they often involve a large number of interactions, it can be difficult to construct such a model for a system, and since the resulting state-level model can involve a huge number of states, model analysis can be difficult or impossible. In this presentation, we introduce methods for the high-level specification of a system using hypergraphs, for the automated generation of a state-level model from a high-level model, and for the exact reduction of a state-level model using information (viz. symmetries and invariant manifolds) from the high-level model. We then give a tutorial demonstration of the practical application of the methods to the modeling of biochemical reaction systems using several examples constructed using Vernan, a MATLAB tool implementing the methods.