We describe the design and operating characteristics of a simple polarized atomic hydrogen beam particularly suitable for applications to crossed beams experiments. In addition to experimental measurements, we present the results of detailed computer models, using Monte-Carlo ray tracing techniques, optical analogs, and phase-space methods, that not only provide us with a confirmation of our measurement, but also allow us to characterize the density, polarization, and atomic fraction of the beam at all points along its path. As a subsidiary result, we also present measurements of the relative and absolute efficiencies of the V/G Supavac mass analyzer for masses 1 and 2.