This article provides the complete description of results from the Phase I data set of the Sudbury Neutrino Observatory (SNO). The Phase I data set is based on a 0.65 kt-year exposure of heavy water to the solar 8B neutrino flux. Included here are details of the SNO physics and detector model, evaluations of systematic uncertainties, and estimates of backgrounds. Also discussed are SNO's approach to statistical extraction of the signals from the three neutrino reactions (charged current, neutral current, and elastic scattering) and the results of a search for a day-night asymmetry in the ?e flux. Under the assumption that the 8B spectrum is undistorted, the measurements from this phase yield a solar ?e flux of ?(?e) = 1.76+0.05?0.05(stat.)+0.09?0.09 (syst.) x 106 cm?2 s?1, and a non-?e component ?(? mu) = 3.41+0.45?0.45(stat.)+0.48?0.45 (syst.) x 106 cm?2 s?1. The sum of these components provides a total flux in excellent agreement with the predictions of Standard Solar Models. The day-night asymmetry in the ?e flux is found to be Ae = 7.0 +- 4.9 (stat.)+1.3?1.2 percent (sys.), when the asymmetry in the total flux is constrained to be zero.