We introduce the Survey for Ionization in Neutral Gas Galaxies (SINGG), a census of star formation in H I selected galaxies. The survey consists of H alpha and R-band imaging of a sample of 468 galaxies selected from the H I Parkes All Sky Survey (HIPASS). The sample spans three decades in H I mass and is free of many of the biases that affect other star-forming galaxy samples. We present the criteria for sample selection, list the entire sample, discuss our observational techniques, and describe the data reduction and calibration methods. This paper focuses on 93 SINGG targets whose observations have been fully reduced and analyzed to date. The majority of these show a single emission line galaxy (ELG). We see multiple ELGs in 13 fields, with up to four ELGs in a single field. All of the targets in this sample are detected in H alpha, indicating that dormant (non-star-forming) galaxies with M-H I greater than or similar to 3x10(7) M-circle dot are very rare. A database of the measured global properties of the ELGs is presented. The ELG sample spans 4 orders of magnitude in luminosity (H alpha and R band), and H alpha surface brightness, nearly 3 orders of magnitude in R surface brightness and nearly 2 orders of magnitude in H alpha equivalent width (EW). The surface brightness distribution of our sample is broader than that of the Sloan Digital Sky Survey (SDSS) spectroscopic sample, the EW distribution is broader than prism-selected samples, and the morphologies found include all common types of star-forming galaxies (e.g., irregular, spiral, blue compact dwarf, starbursts, merging and colliding systems, and even residual star formation in S0 and Sa spirals). Thus, SINGG presents a superior census of star formation in the local universe suitable for further studies ranging from the analysis of H II regions to determination of the local cosmic star formation rate density.