We study how the Fermi energy of a graphene monolayer separated from a conducting substrate by a dielectric spacer depends on the properties of the substrate and on an applied voltage. An analytical model is developed that describes the Fermi level shift as a function of the gate voltage, of the substrate work function, and of the type and thickness of the dielectric spacer. The parameters of this model, that should describe the effect of gate electrodes in field effect devices, can be obtained from density functional theory (DFT) calculations on single layers or interfaces. The doping of graphene in metal|dielectric|graphene structures is found to be determined not only by the difference in work function between the metal and graphene and the dielectric properties of the spacer but potential steps that result from details of the microscopic bonding at the interfaces also play an important role. The doping levels predicted by the model agree very well with the results obtained from first-principles DFT calculations on metal|dielectric|graphene structures with the metals Al, Co, Ni, Cu, Pd, Ag, Pt, or Au, and a h-BN or vacuum dielectric spacer. © 2013 American Physical Society.