We present details on the observing strategy, data-processing techniques, and spectroscopic targeting algorithms for the first three years of operation for the Dark Energy Survey Supernova Program (DES-SN). This five-year program using the Dark Energy Camera mounted on the 4 m Blanco telescope in Chile was designed to discover and follow supernovae (SNe) Ia over a wide redshift range (0.05 z < 1.2) to measure the equation-of-state parameter of dark energy. We describe the SN program in full: strategy, observations, data reduction, spectroscopic follow-up observations, and classification. From three seasons of data, we have discovered 12,015 likely SNe, 308 of which have been spectroscopically confirmed, including 251 SNe Ia over a redshift range of 0.017 z < 0.85. We determine the effective spectroscopic selection function for our sample and use it to investigate the redshift-dependent bias on the distance moduli of SNe Ia we have classified. The data presented here are used for the first cosmology analysis by DES-SN ("DES-SN3YR"), the results of which are given in Dark Energy Survey Collaboration et al. The 489 spectra that are used to define the DES-SN3YR sample are publicly available at .