The VLBI Space Observatory Programme (VSOP) mission is a Japanese-led project to study radio sources with sub-milliarcsecond angular resolution using an orbiting 8 m telescope, HALCA, and global arrays of Earth-based telescopes. Approximately 25% of the observing time has been devoted to a survey of compact active galactic nuclei (AGNs) at 5 GHz that are stronger than 1 Jy - the VSOP AGN Survey. This paper, the second in a series, describes the data calibration, source detection, self-calibration, imaging, and modeling and gives examples illustrating the problems specific to space VLBI. The VSOP Survey Web site, which contains all results and calibrated data, is described.