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 kiloton-year exposure of 2H2O (in the following denoted as D2O) to the solar B8 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 νe flux. Under the assumption that the B8 spectrum is undistorted, the measurements from this phase yield a solar νe flux of (νe)=1.76-0.05+0. 05(stat.)-0.09+0.09(syst.)×106 cm-2 s-1 and a non-νe component of (νμτ)=3.41-0.45+0.45(stat.)-0.45+0.48(syst.)×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 νe flux is found to be Ae=7.0±4.9(stat.)-1.2+1.3%(syst.), when the asymmetry in the total flux is constrained to be zero. © 2007 The American Physical Society.