The results of Multiple Mirror Telescope spectrophotometry of the extremely low metallicity blue compact galaxy (BCG) SBS 0335-052 (SBS-the Second Byurakan Survey) are presented. The oxygen abundance in the central, brightest part of the galaxy is found to be 12 + log (O/H) = 7.33 +/- 0.01, only slightly greater than the oxygen abundance in the most metal-deficient BCG, I Zw 18. We show that the N/O, Ne/O, S/O, and Ar/O abundance ratios in SBS 0335-052 are close to those derived for other BCGs, suggesting that heavy-element enrichment in the H II region is due to massive-star evolution. However, we find an O/Fe abundance ratio close to that in the Sun, at variance with values derived for other BCGs. The helium abundance derived from the He I 4471, 5876, and 6678 Angstrom emission lines, taking into account collisional and fluorescent enhancement, is Y = 0.245 +/- 0.006, close to the value of the primordial helium abundance, Y-p = 0.243 +/- 0.003, derived by Izotov, Thuan, & Lipovetsky. We detect auroral [O III] lambda 4363 emission in the inner part of the H II region with a diameter of 14 '', or 3.6 kpc, and find that the H II region inside this diameter is hot, T-e similar to 20,000 K. The oxygen abundance in this region is nearly constant [12 + log (O/H)= 7.1-7.3], with a gradual decrease to the outer part of II II region, implying effective mixing of ionized gas on short timescales. We study the distribution;of the nebular He II lambda 4686 emission line and find that it is not produced by main-sequence O stars or Wolf-Rayet stars. Possible excitation mechanisms for this line, such as massive X-ray binaries and shocks, are discussed. We also discuss the origin of blue, underlying, extended low-intensity emission detected in SBS 0335-052 in V, R, and I images. The blue V-I and R-I color distributions suggest that a significant contribution to the extended low-intensity envelope is due to ionized gas emission. This is evidence that SBS 0335-052 is a young galaxy experiencing its very first burst of star formation. However, we find that the observed equivalent width of H beta emission in the extended envelope is 2-3 times lower than the value expected in the case of pure gaseous emission. Furthermore, we find that the widths of H gamma and H beta are narrower than the instrumental process; this could be explained by the presence of underlying stellar absorption from A stars. These findings suggest that, along with the young (similar to 10(7) yr) blue stellar clusters in the center of the galaxy, an older stellar population of age similar to 10(8) yr may be present in the extended envelope of SBS 0335-052 having a total mass of similar to 10(7) M., 2 orders of magnitude smaller than the neutral gas mass but comparable with the total mass of stars in blue young stellar clusters observed in the center of the galaxy. We conclude that SBS 0335-052 is a young nearby dwarf galaxy with age similar to 10(8) yr.