We have started a search for supernovae as a collaboration between the University of Chile and the Cerro Tololo Inter-American Observatory, with the aim of producing a moderately distant (0.01 < z < 0.10) sample of Type Ia and Type II supernovae suitable for cosmological studies. The project began in mid-1990 and continues to the present. This paper reports on the Calan/Tololo discoveries in the course of 1990, and on the spectroscopic and photometric observations gathered for these objects. All of these observations were obtained with CCDs, with the extensive collaboration of visiting astronomers. Great care was exercised in the reduction of the light curves in order to properly correct for the background light of the host galaxy of each supernova. Of the four supernovae found in 1990, one proved to be a SN II-n; the remaining three were members of the Type Ia class at redshifts that ranged between z = 0.04-0.05. One of the Type Ia events, SN 1990af, was found in the elusive premaximum phase at a redshift of z = 0.0503, and was observed through maximum light. Peak magnitudes for the other two SNe Ia, which were not observed at maximum light, were derived using a chi2 minimization technique to fit the data with various template curves that represent a broad range of SNe Ia light curves. In future papers we will make use of these estimates in order to discuss the Hubble diagram of SNe Ia.