We present a technique to fabricate tunnel junctions between graphene and Al and Cu, with a Si backgate, as well as a simple theory of tunneling between a metal and graphene. We map the differential conductance of our junctions versus probe and backgate voltage, and observe fluctuations in the conductance that are directly related to the graphene density of states. The conventional strong-suppression of the conductance at the graphene Dirac point cannot be clearly demonstrated, but a more robust signature of the Dirac point is found: the inflection in the conductance map caused by the electrostatic gating of graphene by the tunnel probe. We present numerical simulations of our conductance maps, confirming the measurement results. In addition, Al causes strong n doping of graphene, Cu causes a moderate p doping, and in high resistance junctions, phonon resonances are observed, as in STM studies.