The Apache Point Observatory Galactic Evolution Experiment (APOGEE) is a high-resolution infrared spectroscopic survey spanning all Galactic environments (i.e., bulge, disk, and halo), with the principal goal of constraining dynamical and chemical evolution models of the Milky Way. APOGEE takes advantage of the reduced effects of extinction at infrared wavelengths to observe the inner Galaxy and bulge at an unprecedented level of detail. The survey's broad spatial and wavelength coverage enables users of APOGEE data to address numerous Galactic structure and stellar populations issues. In this paper we describe the APOGEE targeting scheme and document its various target classes to provide the necessary background and reference information to analyze samples of APOGEE data with awareness of the imposed selection criteria and resulting sample properties. APOGEE's primary sample consists of ~105 red giant stars, selected to minimize observational biases in age and metallicity. We present the methodology and considerations that drive the selection of this sample and evaluate the accuracy, efficiency, and caveats of the selection and sampling algorithms. We also describe additional target classes that contribute to the APOGEE sample, including numerous ancillary science programs, and we outline the targeting data that will be included in the public data releases.