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We present results on the location, physical conditions, and geometry of the outflow in the Seyfert 1 galaxy NGC 3783 from a study of the variable intrinsic UV absorption. Based on analysis of 18 observations with the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope and six observations with the Far Ultraviolet Spectroscopic Explorer obtained between 2000 February and 2002 January, we obtain the following results: (1) The lowest ionization species detected in each of the three strong kinematic components (components 1-3 at radial velocities -1350, -550, and -725 km/s, respectively) varied, with equivalent widths inversely correlated with the continuum flux. This indicates that the ionization structure in the absorbers responded to changes in the photoionizing flux, with variations occurring over the weekly timescales sampled by our observations. (2) A multicomponent model of the line-of-sight absorption covering factors, which includes an unocculted narrow emission-line region (NLR) and separate covering factors derived for the broad-line region and continuum emission sources, predicts saturation in several lines, consistent with the lack of observed variability in these lines. Differences in covering factors and kinematic structure imply that component 1 is composed of two physically distinct regions (1a and 1b). (3) We obtain column densities for the individual metastable levels from the resolved C III* λ1175 absorption complex in component 1a. Based on our computed metastable level populations, the electron density of this absorber is ∼3x10⁴/cm3. Combined with photoionization modeling results, this places component 1a at ∼25 pc from the central source. (4) Using time-dependent calculations, we are able to reproduce the detailed variability observed in component 1 and derive upper limits on the distances for components 2 and 3 of ≤25 and ≤50 pc, respectively. (5) The ionization parameters derived for the higher ionization UV absorbers (components 1b, 2, and 3 with logU~-0.5) are consistent with the modeling results for the lowest ionization X-ray component, but with smaller total column density. The high-ionization UV components are found to have pressures similar to those of the three X-ray ionization components. These results are consistent with an inhomogeneous wind model for the outflow in NGC 3783, with denser, colder, lower ionization regions embedded in more highly ionized gas. (6) Based on the predicted emission-line luminosities, global covering factor constraints, and distances derived for the UV absorbers, they may be identified with emission-line gas observed in the inner NLR of AGNs. We explore constraints for dynamical models of AGN outflows implied by these results.