We present HST WFPC2 V and I images and GHRS UV spectrophotometry of the spectral regions around Ly alpha and O I lambda 1302 of the extremely metal-deficient (Z similar to Z./41) blue compact dwarf galaxy (BCD) SBS 0335-052. All the star formation in the BCD occurs in six super-star clusters (SSCs) with ages less than or equal to 25 Myr, within a region of similar to 2'' or 520 pc in size. Dust is clearly present and mixed spatially with the SSCs. The SSCs are roughly aligned in the southeast-northwest direction, and there is a systematic increase in reddening of the clusters away from the brightest one. The observed color dependence on position may be the combined effects of differential extinction by dust and color evolution with time due to sequential propagating star formation. There is a supershell of radius similar to 380 pc, delineating a large supernova cavity. The instantaneous star formation rate is similar to 0.4 M. yr(-1). Strong narrow Ly alpha emission is not observed. Rather there is low-intensity broad (FWZI = 20 Angstrom) Ly alpha emission superposed on even broader Ly alpha absorption by the H I envelope. This broad low-intensity emission is caused by resonant scattering of Ly alpha photons. The absence of strong Ly alpha emission may be due partly to dust absorption, but is due mainly to multiple scattering that removes Ly alpha photons from the small HST aperture. As the H I cloud is seen nearly edge-on, geometrical effects may also play a role as photons escape more easily in a direction perpendicular to the plane than along it. The BCD appears to be a young galaxy, undergoing one of its very first bursts of star formation. This conclusion is based on the following evidence: (1) The underlying extended low surface brightness component is irregular and filamentary, suggesting that a significant part of the emission comes from ionized gas. Any underlying stellar population must be younger than similar to 10(8) yr. (2) The underlying component has very blue colors [-0.34 less than or equal to (V-I)(0) less than or equal to 0.16], consistent with gaseous emission colors. (3) The O I lambda 1302 line is not detected in absorption in the Goddard High Resolution Spectrograph spectrum, setting an upper limit for N(O)/N(H) in the H I envelope of the BCD of more than 3000 times smaller than the value in Orion.