The ACS Survey of Globular Clusters has used Hubble Space Telescope's Wide-Field Channel to obtain uniform imaging of 65 of the nearest globular clusters to provide an extensive homogeneous data set for a broad range of scientific investigations. The survey goals required not only a uniform observing strategy, but also a uniform reduction strategy. To this end, we designed a sophisticated software program to process the cluster data in an automated way. The program identifies stars simultaneously in the multiple dithered exposures for each cluster and measures them using the best available point-spread function models. We describe here in detail the program's rationale, algorithms, and output. The routine was also designed to perform artificial-star tests, and we ran a standard set of ~105 tests for each cluster in the survey. The catalog described here will be exploited in a number of upcoming papers and will eventually be made available to the public via the World Wide Web. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555.