The Gemini Planet Imager (GPI) has as its science instrument an infrared integral field spectrograph/polarimeter (IFS). Integral field spectrographs are scientificially powerful but require sophisticated data reduction systems. For GPI to achieve its scientific goals of exoplanet and disk characterization, IFS data must be reconstructed into high quality astrometrically and photometrically accurate datacubes in both spectral and polarization modes, via flexible software that is usable by the broad Gemini community. The data reduction pipeline developed by the GPI instrument team to meet these needs is now publicly available following GPI's commissioning. This paper, the first of a series, provides a broad overview of GPI data reduction, summarizes key steps, and presents the overall software framework and implementation. Subsequent papers describe in more detail the algorithms necessary for calibrating GPI data. The GPI data reduction pipeline is open source, available from planetimager.org, and will continue to be enhanced throughout the life of the instrument. It implements an extensive suite of task primitives that can be assembled into reduction recipes to produce calibrated datasets ready for scientific analysis. Angular, spectral, and polarimetric differential imaging are supported. Graphical tools automate the production and editing of recipes, an integrated calibration database manages reference files, and an interactive data viewer customized for high contrast imaging allows for exploration and manipulation of data.