The initial stages of water adsorption on the Pd(111) and Ru(0001) surfaces have been investigated experimentally by scanning tunneling microscopy in the temperature range between 40 and 130 K, and theoretically with density functional theory (DFT) total energy calculations and scanning tunneling microscopy (STM) image simulations. Below 125 K, water dissociation does not occur at any appreciable rate, and only molecular films are formed. Film growth starts by the formation of flat hexamer clusters where the molecules bind to the metal substrate through the O-lone pair while making H-bonds with neighboring molecules. As coverage increases, larger networks of linked hexagons are formed with a honeycomb structure, which requires a fraction of the water molecules to have their molecular plane perpendicular to the metal surface with reduced water-metal interaction. Energy minimization favors the growth of networks with limited width. As additional water molecules adsorb on the surface, they attach to the periphery of existing islands, where they interact only weakly with the metal substrate. These molecules hop along the periphery of the clusters at intermediate temperatures. At higher temperatures, they bind to the metal to continue the honeycomb growth. The water-Ru interaction is significantly stronger than the water-Pd interaction, which is consistent with the greater degree of hydrogen-bonded network formation and reduced water-metal bonding observed on Pd relative to Ru.