The Sloan Digital Sky Survey-II Supernova Survey has identified a large number of new transient sources in a 300 deg2 region along the celestial equator during its first two seasons of a three-season campaign. Multi-band (ugriz) light curves were measured for most of the sources, which include solar system objects, galactic variable stars, active galactic nuclei, supernovae (SNe), and other astronomical transients. The imaging survey is augmented by an extensive spectroscopic follow-up program to identify SNe, measure their redshifts, and study the physical conditions of the explosions and their environment through spectroscopic diagnostics. During the survey, light curves are rapidly evaluated to provide an initial photometric type of the SNe, and a selected sample of sources are targeted for spectroscopic observations. In the first two seasons, 476 sources were selected for spectroscopic observations, of which 403 were identified as SNe. For the type Ia SNe, the main driver for the survey, our photometric typing and targeting efficiency is 90%. Only 6% of the photometric SN Ia candidates were spectroscopically classified as non-SN Ia instead, and the remaining 4% resulted in low signal-to-noise, unclassified spectra. This paper describes the search algorithm and the software, and the real-time processing of the SDSS imaging data. We also present the details of the supernova candidate selection procedures and strategies for follow-up spectroscopic and imaging observations of the discovered sources.