In this paper, we present theoretical and computational details of implementing the recently developed reactant-product decoupling (RPD) method (J. Chem. Phys. 105, 6072 (1996)) for state-to-state quantum reactive scattering calculations of the prototypical H + H-2 reaction in three dimensions. The main purpose of this paper is to explore important features of the RPD scheme for use as a general and efficient computational approach to study state-to-state quantum dynamics for polyatomic reactions by using 3D H + H-2 as an example. Specific computational techniques and numerical details are explicitly provided for efficient application of this method in the time-dependent (TD) implementation. Using the RPD method, the calculated state-to-state reaction probabilities for the 3D H + H-2 reaction are in excellent agreement with those from the time-independent variational calculations, and the computational cost of the RPD method is significantly lower than other existing TD methods for state-to-state dynamics calculations.