Absorption-line spectroscopy is a powerful tool used to estimate element abundances in the nearby as well as distant universe. The accuracy of the abundances thus derived is, naturally, limited by the accuracy of the atomic data assumed for the spectral lines. We have recently started a project to perform the new extensive atomic data calculations used for optical/UV spectral lines in the plasma modeling code Cloudy using state-of-the-art quantal calculations. Here we demonstrate our approach by focussing on S II, an ion used to estimate metallicities for Milky Way interstellar clouds as well as distant damped Lyman-alpha (DLA) and sub-DLA absorber galaxies detected in the spectra of quasars and gamma-ray bursts (GRBs). We report new extensive calculations of a large number of energy levels of S II, and the line strengths of the resulting radiative transitions. Our calculations are based on the configuration interaction approach within a numerical Hartree-Fock framework, and utilize both non-ralativistic and quasirelativistic one-electron radial orbitals. The results of these new atomic calculations are then incorporated into Cloudy and applied to a lab plasma, and a typical DLA, for illustrative purposes. The new results imply relatively modest changes (~0.04 dex) to the metallicities estimated from S II in past studies. These results will be readily applicable to other studies of S II in the Milky Way and other galaxies.