A long-standing aspect of collegiate culture at many advanced-degree-granting universities is the use of Graduate Teaching Assistants (GTAs) to teach an introductory course. This practice presents a serious pedagogical challenge--namely, how to train inexperienced GTAs to teach the course. Too often new GTAs are merely supplied with the textbook and told to "go teach." A more productive response to the challenge is to teach an intensive graduate workshop required of all GTAs on the pedagogy of the introductory course. This paper describes the philosophy and methodology of one such workshop with a successful track record of nearly 30 years to train GTAs to teach the basic (public speaking) course. (Contains 32 references. Appendixes contain course requirements; the undergraduate syllabus course outline; an excerpt from the basic course curriculum guide; and an excerpt from the GTA workshop syllabus.) (Author/RS)