A detailed procedure is described for computing discrete equations of motion for a fluid, to implement a new method which turns out to be substantially more efficient than previous methods for calculating transport coefficients. This paper describes the calculations of discrete averages from molecular dynamics data and the numerical extraction of the equation-of-motion coefficients in a way which makes maximum use of the geometric symmetry of the problem. Extrapolation to the infinite-system limit and eventual computation of transport coefficients by renormalization are discussed. The method described in detail here is briefly sketched and applied numerically to computing the viscosity of the soft-sphere liquid in a subsequent paper.