This chapter originates from a set of notes developed by the author for the members of Allen Bard’s research group at the University of Texas in the late 1960s. Based entirely upon the pioneering research of Steve Feldberg [1–3], this work began as a how-to guide for those who wanted to learn how to write the computer code to perform digital simulations of electrochemical phenomena. These notes then circulated underground for more than a decade while the first edition of this text was in preparation. During that period, numerous practitioners of the art used these notes, or materials based upon them [4], as an introduction to digital simulation. It was in this pedagogical milieu that the version found in the first edition was written.