We report on the NASA Astrobiology Institute-funded Workshop Without Walls entitled "Stellar Stoichiometry," hosted by the "Follow the Elements" team at Arizona State University in April 2013. We describe several innovative practices we adopted that made effective use of the Workshop Without Walls videoconferencing format, including use of information technologies, assignment of scientific tasks before the workshop, and placement of graduate students in positions of authority. A companion article will describe the scientific results arising from the workshop. Our intention here is to suggest best practices for future Workshops Without Walls.