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We report spectroscopic and photometric observations of the Type IIb SN 2011dh obtained between 4 and 34 days after the estimated date of explosion (May 31.5 UT). The data cover a wide wavelength range from 2000 Å in the ultraviolet (UV) to 2.4 μm in the near-infrared (NIR). Optical spectra provide line profiles and velocity measurements of H I, He I, Ca II, and Fe II that trace the composition and kinematics of the supernova (SN). NIR spectra show that helium is present in the atmosphere as early as 11 days after the explosion. A UV spectrum obtained with the Space Telescope Imaging Spectrograph reveals that the UV flux for SN 2011dh is low compared to other SN IIb. Modeling the spectrum with SYNOW suggests that the UV deficit is due to line blanketing from Ti II and Co II. The H I and He I velocities in SN 2011dh are separated by about 4000 km s–1 at all phases. A velocity gap is consistent with models for a preexplosion structure in which a hydrogen-rich shell surrounds the progenitor. We estimate that the H shell of SN 2011dh is ≈8 times less massive than the shell of SN 1993J and ≈3 times more massive than the shell of SN 2008ax. Light curves (LCs) for 12 passbands are presented: UVW2, UVM2, UVW1, U, u′, B, V, r′, i′, J, H, and Ks. In the B band, SN 2011dh reached peak brightness of 13.17 mag at 20.0 ± 0.5 after the explosion. The maximum bolometric luminosity of 1.8 ± 0.2 × 1042 erg s–1 occurred ≈22 days after the explosion. NIR emission provides more than 30% of the total bolometric flux at the beginning of our observations, and the NIR contribution increases to nearly 50% of the total by day 34. The UV produces 16% of the total flux on day 4, 5% on day 9, and 1% on day 34. We compare the bolometric LCs of SN 2011dh, SN 2008ax, and SN 1993J. The LC are very different for the first 12 days after the explosions, but all three SN IIb display similar peak luminosities, times of peak, decline rates, and colors after maximum. This suggests that the progenitors of these SN IIb may have had similar compositions and masses, but they exploded inside hydrogen shells that have a wide range of masses. SN 2011dh was well observed, and a likely progenitor star has been identified in preexplosion images. The detailed observations presented here will help evaluate theoretical models for this SN and lead to a better understanding of SN IIb. [ABSTRACT FROM AUTHOR]