We present extensive early photometric (ultraviolet through near-infrared) and spectroscopic (optical and near-infrared) data on supernova (SN) 2008D as well as X-ray data analysis on the associated Swift/X-ray transient (XRT) 080109. Our data span a time range of 5 hours before the detection of the X-ray transient to 150 days after its detection, and detailed analysis allowed us to derive constraints on the nature of the SN and its progenitor; throughout we draw comparisons with results presented in the literature and find several key aspects that differ. We show that the X-ray spectrum of XRT 080109 can be fit equally well by an absorbed power law or a superposition of about equal parts of both power law and blackbody. Our data first established that SN 2008D is a spectroscopically normal SN Ib (i.e., showing conspicuous He lines), and show that SN 2008D had a relatively long rise time of 18 days and a modest optical peak luminosity. The early-time light curves of the SN are dominated by a cooling stellar envelope (for Delta t~0.1- 4 day, most pronounced in the blue bands) followed by 56^Ni decay. We construct a reliable measurement of the bolometric output for this stripped-envelope SN, and, combined with estimates of E_K and M_ej from the literature, estimate the stellar radius R_star of its probable Wolf-Rayet progenitor. According to the model of Waxman et al. and of Chevalier & Fransson, we derive R_star^{W07}= 1.2+/-0.7 R_sun and R_star^{CF08}= 12+/-7 R_sun, respectively; the latter being more in line with typical WN stars. Spectra obtained at 3 and 4 months after maximum light show double-peaked oxygen lines that we associate with departures from spherical symmetry, as has been suggested for the inner ejecta of a number of SN Ib cores.