We present new results on the kinematics and spatial distribution of metal-enriched gas within ~125 kpc of star-forming ("Lyman break") galaxies at redshifts 2 ≲ z ≲ 3. In particular, we focus on constraints provided by the rest-frame far-ultraviolet (far-UV) spectra of faint galaxies, and demonstrate how galaxy spectra can be used to obtain key spatial and spectral information more efficiently than possible with QSO sightlines. Using a sample of 89 galaxies with z = 2.3 ± 0.3 and with both rest-frame far-UV and Hα spectra, we re-calibrate the measurement of accurate galaxy systemic redshifts using only survey-quality rest-UV spectra. We use the velocity-calibrated sample to investigate the kinematics of the galaxy-scale outflows via the strong interstellar (IS) absorption lines and Lyα emission (when present), as well as their dependence on other physical properties of the galaxies. We construct a sample of 512 close (1"-15") angular pairs of z ~ 2-3 galaxies with redshift differences indicating a lack of physical association. Sightlines to the background galaxies provide new information on the spatial distribution of circumgalactic gas surrounding the foreground galaxies. The close pairs sample galactocentric impact parameters 3-125 kpc (physical) at = 2.2, providing for the first time a robust map of cool gas as a function of galactocentric distance for a well-characterized population of galaxies. We propose a simple model of circumgalactic gas that simultaneously matches the kinematics, depth, and profile shape of IS absorption and Lyα emission lines, as well as the observed variation of absorption line strength (H I and several metallic species) versus galactocentric impact parameter. Within the model, cool gas is distributed symmetrically around every galaxy, accelerating radially outward with v_(out)(r) increasing with r (i.e., the highest velocities are located at the largest galactocentric distances r). The inferred radial dependence of the covering fraction of cool gas (which modulates the absorption line strength) is f_c(r) ∝ r^(–γ) with 0.2 ≲ γ ≲ 0.6 depending on transition. We discuss the results of the observations in the context of "cold accretion," in which cool gas is accreting via filamentary streams directly onto the central regions of galaxies. At present, we find little observational evidence for cool infalling material, while evidence supporting the large-scale effects of superwind outflows is strong. This "pilot" study using faint galaxy spectra demonstrates the potential of using galaxies to trace baryons within galaxies, in the circumgalactic medium, and ultimately throughout the intergalactic medium