The study of catalytic behavior begins with one seemingly simple process, namely the hydrogenation of O to H2O on platinum. Despite the apparent simplicity its mechanism has been much debated. We have used density functional theory with gradient corrections to examine microscopic reaction pathways for several elementary steps implicated in this fundamental catalytic process. We find that H2O formation from chemisorbed O and H atoms is a highly activated process. The largest barrier along this route, with a value of approximately 1 eV, is the addition of the first H to O to produce OH. Once formed, however, OH groups are easily hydrogenated to H2O with a barrier of approximately 0.2 eV. Disproportionation reactions with 1:1 and 2:1 stoichiometries of H2O and O have been examined as alternative routes for OH formation. Both stoichiometries of reaction produce OH groups with barriers that are much lower than that associated with the O + H reaction. H2O, therefore, acts as an autocatalyst in the overall H2O formation process. Disproportionation with a 2:1 stoichiometry is thermodynamically and kinetically favored over disproportionation with a 1:1 stoichiometry. This highlights an additional (promotional) role of the second H2O molecule in this process. In support of our previous suggestion that the key intermediate in the low-temperature H2O formation reaction is a mixed OH and H2O overlayer we find that there is a very large barrier for the dissociation of the second H2O molecule in the 2:1 disproportionation process. We suggest that the proposed intermediate is then hydrogenated to H2O through a very facile proton-transfer mechanism.