The structure of water near a synthetic clay surface, Laponite, is probed experimentally by total neutron scattering, in both liquid and arrested states. It is shown that the crystalline structure of the Laponite platelets and their charge distribution determine polarization of the closest water layers, with a local density higher than that of bulk water. Interestingly these layers show long range order in the plane parallel to the Laponite surface, while no indication of strong hydrogen bonding between water and Laponite is found.