DESY Hamburg operates a test beam facility with three independent beam lines at the DESY II synchrotron. It is world-wide one of very few facilities providing test beams in the GeV range. To this end, it offers electron/positron beams with user-selectable momenta from 1-6 GeV/c. The available infrastructure for the users is unique, including a high field solenoidal magnet and permanently installed high-precision pixel beam telescopes. This publication gives a detailed description of the facility, the available infrastructure, and the simulated and measured performance.