Optical observations of the transient X-ray source A0620-00 over the wavelength range from about 3200 to 6600 A are analyzed which were made with the 5-m Hale telescope using a multichannel spectrometer, a digital spectrograph with a cooled integrating SIT vidicon, and an image photon-counting system attached to the camera of the coude spectrograph. Infrared observations at 1.65, 2.2, and 3.5 microns are also examined. Individual spectral lines of special interest are discussed, the E(B-V) color excess is estimated to be about 0.40, and a distance of 1200 pc is adopted. Analysis of the continuous spectrum yields several simple binary models. A specific model is proposed in which one of the continuum sources is an optically thick object characterized by a model atmosphere at a temperature of 25,000 to 30,000 K and the second source is either a cool black body at 4000 K or a partially optically thick source of bound-free plus free-free radiation from a hydrogen gas with an electron temperature of at least 100,000 K. Some possible parameters of these sources and of the accretion disk are considered.