The Qweak experiment will provide the most precise determination of the proton’s weak charge Q^p_W by measuring the parity-violating asymmetry in elastic electron-proton scattering at low momentum transfer Q^2 = 0.0250 (GeV/c)^2. Qpw is related to the weak mixing angle sin^2\theta_W, a fundamental parameter of the standard model. A final measurement of the weak charge at the proposed 4% relative uncertainty is sensitive to certain types of new parity-violating physics beyond the standard model at the TeV mass-scale. Data were taken over a two year period beginning in 2010, using a custom apparatus installed in Hall-C at the Thomas Jefferson National Accelerator Facility in Newport News, Virginia. A 180 microamp beam of longitudinally polarized electrons was accelerated to 1.165 GeV and then scattered from unpolarized protons in a liquid hydrogen target. The scattered electrons were then collimated and steered using a magnetic spectrometer onto a set of azimuthally symmetric quartz bar Cherenkov detectors. The performance of this main detector subsystem will be described in detail in this dissertation. A blinded analysis of Run-II, roughly 2/3 of the entire Qweak data set, resulted in an elastic ep asymmetry of -235.6 +/- 8.7 (Stat) +/- 9.3 (Syst.) +/- 39.3 (Blind) ppb. Using this value, the proton’s weak charge was calculated to be QpW = 0.0714 +/- 0.0093. This constitutes a 17% relative measurement, that will reduce to < 9% upon unblinding the asymmetry. This dissertation will provide the details that went into extracting both the parity-violating asymmetry and the weak charge of the proton.