The Apache Point Observatory Galactic Evolution Experiment (APOGEE), part of the Sloan Digital Sky Survey III, explores the stellar populations of the Milky Way using the Sloan 2.5-m telescope linked to a high resolution (R ∼ 22,500), near-infrared (1.51–1.70 μm) spectrograph with 300 optical fibers. For over 150,000 predominantly red giant branch stars that APOGEE targeted across the Galactic bulge, disks and halo, the collected high signal-to-noise ratio (>100 per half-resolution element) spectra provide accurate (∼0.1 km s‑1) RVs, stellar atmospheric parameters, and precise (≲0.1 dex) chemical abundances for about 15 chemical species. Here we describe the basic APOGEE data reduction software that reduces multiple 3D raw data cubes into calibrated, well-sampled, combined 1D spectra, as implemented for the SDSS-III/APOGEE data releases (DR10, DR11 and DR12). The processing of the near-IR spectral data of APOGEE presents some challenges for reduction, including automated sky subtraction and telluric correction over a 3°-diameter field and the combination of spectrally dithered spectra. We also discuss areas for future improvement.