A theoretical model is developed for the description of the single-electron emission from surfaces following the impact of fast ions. The theory describes quantum mechanically the ion reflection at the surface and the excitation of the valence band electrons via an ion-electron interaction renormalized by the dielectric response of the target. Numerical calculations are presented and analyzed for the electron emission from the conduction band of an aluminium surface upon proton impact. Particular attention is devoted to the influence of the dielectric screening of the energy distributions and the angular distributions of the ejected electrons. In addition, the role of the surface electronic structure is studied.