The polyhedral homotopy method is known to be a powerful numerical method for approximating all isolated solutions of a system of polynomial equations. We discuss a parallel implementation of the polyhedral homotopy method, a dynamic enumeration of all fine mixed cells which is used in constructing a family of polyhedral homotopy functions and extensions of the Hornor Scheme to multivariate polynomials for efficient evaluation of a system of polynomials and their partial derivatives in the polyhedral homotopy method.