General aspects of the H1 detector at the electron-proton storage ring HERA as well as technical descriptions of the magnet, luminosity system, trigger, slow-control, data acquisition and off-line data handling are given. The three major components of the detector, the tracking, calorimeter and muon detectors, will be described in a forthcoming article. The present paper describes the detector that was used from 1992 to the end of 1994. After this a major upgrade of some components was undertaken. Some performance figures from luminosity runs at HERA during 1993 and 1994 are given.