We have monitored the evolution of the transient X-ray source GRO J0422 + 32 from approximately 2 weeks postdiscovery into its early decline phase at ultraviolet, optical, and radio wavelengths. Optical and ultraviolet spectra exhibit numerous, but relatively weak, high-excitation emission lines such as those arising from He II, N III, N V, and C IV superposed on an intrinsically blue continuum. High-resolution optical spectroscopy reveals line profiles which are double peaked, and in the case of the higher order Balmer lines, superposed on a broad absorption profile. The early outburst optical-ultraviolet continuum energy distribution is well represented by a two power-law fit with a break at congruent-to 4000 angstrom. Radio observations with the VLA reveal a flat-spectrum source, slowly increasing in intensity at the earliest epochs observed, followed by an approximate power-law decay light curve with an index of - 1. Light curves for each wavelength domain are presented and discussed. Notable are the multiple secondary outbursts seen in the optical more than 1 year postdiscovery, and spectral changes associated with secondary rises seen in the radio and UV. We find that the ultraviolet and optical characteristics of GRO J0422 + 32 as well as its radio evolution, are similar to other recent well-observed soft X-ray transients (also called X-ray novae) such as Cen X-4, A0620-00 (V616 Mon), and Nova Muscae 1991 (GS 1124-683), suggesting that GRO J0422 + 32 is also a member of that subclass of low-mass X-ray binaries. We present definitive astrometric determination of the source position, and place an upper limit of R congruent-to 20 from our analysis of the POSS. Additionally, we derive distinct values for color excess from analysis of the optical [E(B - V) = 0.23] and ultraviolet [E(B - V) = 0.4] data, suggesting an intrinsic magnitude of 19-19.5 for the progenitor if it is mid-K dwarf. This leads to a likely range of 2.4-3.0 kpc for the source distance, which is consistent with our separate estimate of 2.4 +/- 0.4 kpc based on measurement of the NaD interstellar line profile. Adopting 2.4 kpc and E(B - V ) = 0.23, the outburst absolute magnitude was M congruent-to 0.0, which is a typical value for this class of objects.