The process by which supercooled fluids form stable, crystalline solids has been found to be elusive both experimentally and via computer simulations. This is because this process, generally called nucleation, is statistical in nature and because the set of intermediate states, generally called the critical nucleus, is very short-lived. Thus, there are very large uncertainties in even the limited experimental data that exist, and computer simulations that have been performed can yield descriptive information at best. Here we present a detailed and quantitatively accurate observation of the most important nucleation process, the freezing of liquid water at ambient conditions. We have accomplished this by using a method based on choosing a suitable set of order parameters to characterize the crystallinity of the system and a non-Boltzmann sampling Monte Carlo approach to obtain a statistical average of the properties of the system during its transition from liquid to ice (I-h). We have characterized the order of the system statistically at intermediate states between liquid water and ice I-h and in so doing described the nucleation process.