We describe the design and data analysis of the DEEP2 Galaxy Redshift Survey, the densest and largest high-precision redshift survey of galaxies at z ∼ 1 completed to date. The survey was designed to conduct a comprehensive census of massive galaxies, their properties, environments, and large-scale structure down to absolute magnitude MB = -20 at z ∼ 1 via ∼90 nights of observation on the Keck telescope. The survey covers an area of 2.8 deg2 divided into four separate fields observed to a limiting apparent magnitude of RAB = 24.1. Objects with z ≲ 0.7 are readily identifiable using BRI photometry and rejected in three of the four DEEP2 fields, allowing galaxies with z > 0.7 to be targeted ∼2.5 times more efficiently than in a purely magnitude-limited sample. Approximately 60% of eligible targets are chosen for spectroscopy, yielding nearly 53,000 spectra and more than 38,000 reliable redshift measurements. Most of the targets that fail to yield secure redshifts are blue objects that lie beyond z ∼ 1.45, where the [O II] 3727 Å doublet lies in the infrared. The DEIMOS 1200 line mm-1 grating used for the survey delivers high spectral resolution (R ∼ 6000), accurate and secure redshifts, and unique internal kinematic information. Extensive ancillary data are available in the DEEP2 fields, particularly in the Extended Groth Strip, which has evolved into one of the richest multiwavelength regions on the sky. This paper is intended as a handbook for users of the DEEP2 Data Release 4, which includes all DEEP2 spectra and redshifts, as well as for the DEEP2 DEIMOS data reduction pipelines. Extensive details are provided on object selection, mask design, biases in target selection and redshift measurements, the spec2d two-dimensional data-reduction pipeline, the spec1d automated redshift pipeline, and the zspec visual redshift verification process, along with examples of instrumental signatures or other artifacts that in some cases remain after data reduction. Redshift errors and catastrophic failure rates are assessed through more than 2000 objects with duplicate observations. Sky subtraction is essentially photon-limited even under bright OH sky lines; we describe the strategies that permitted this, based on high image stability, accurate wavelength solutions, and powerful B-spline modeling methods. We also investigate the impact of targets that appear to be single objects in ground-based targeting imaging but prove to be composite in Hubble Space Telescope data; they constitute several percent of targets at z ∼ 1, approaching ∼5%-10% at z > 1.5. Summary data are given that demonstrate the superiority of DEEP2 over other deep high-precision redshift surveys at z ∼ 1 in terms of redshift accuracy, sample number density, and amount of spectral information. We also provide an overview of the scientific highlights of the DEEP2 survey thus far. © 2013. The American Astronomical Society. All rights reserved.