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 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 ν_e flux. Under the assumption that the ⁸B spectrum is undistorted, the measurements from this phase yield a solar ν_e flux of φ(ν_e) = 1.76-0.05+0.05(stat.)-0.09+0.09(syst.)×10⁶ cm^-2 s^-1 and a non-ν_e component of φ(ν_μτ) = 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 ν_e flux is found to be A_e = 7.0±4.9(stat.)-1.2+1.3%(syst.), when the asymmetry in the total flux is constrained to be zero.