The recently completed Qweak experiment at Jefferson Laboratory made the first direct determination of the proton's weak charge, QpW, via a measurement of the parity-violating asymmetry in elastic electron-proton scattering at low four-momentum transfer. The Standard Model (SM) makes a precise prediction of QpW (SM) = 0.0710 ± 0.0007. A deviation from this prediction could be an indicator of new physics. A longitudinally polarized electron beam was scattered off a liquid hydrogen target and detected in eight azimuthally symmetric fused silica detectors. The small asymmetry, Aep = -279 ± 35 (stat) ±31 (syst) ppb, was measured by observing the difference in rates seen in the detectors when the helicity of the electron beam was rapidly reversed. The measured asymmetry is the most precise and smallest asymmetry ever measured in an e⃗p scattering experiment. Combining this asymmetry with previous parity- violating electron scattering (PVES) data, we obtained a value of QpW(PVES) = 0.064 ± 0.012, which agrees well with the SM value. The results of the experiment's commissioning run, which constitutes about 4% of the total data set, are reported here. Analysis of the remainder of the data set is ongoing and will significantly reduce the statistical and systematic uncertainties; several aspects of this analysis will be highlighted.