The observation of a prompt optical flash from GRB 990123 convincingly demonstrated the value of autonomous robotic telescope systems. Pursuing a program of rapid follow-up observations of gamma-ray bursts, the Robotic Optical Transient Search Experiment (ROTSE) has developed a next-generation instrument, ROTSE-III, that will continue the search for fast optical transients. The entire system was designed as an economical robotic facility to be installed at remote sites throughout the world. There are seven major system components: optics, optical tube assembly, CCD camera, telescope mount, enclosure, environmental sensing and protection, and data acquisition. Each is described in turn in the hope that the techniques developed here will be useful in similar contexts elsewhere.