We report the development of an experimental technique to measure the dynamics of electrical currents on the femtosecond timescale. The technique combines methods of coherent control with time- and angle-resolved photoelectron spectroscopy. Direct snapshots of the momentum distribution of the excited electrons as function of time are then determined by photoelectron spectroscopy. In this way we gain information on the generation and decay of ultrashort current pulses in unprecedented detail. In particular, this technique allows the observation of elastic electron scattering in terms of an incoherent population dynamics in momentum space. We have applied this optical current generation and detection scheme to electrons in so-called image-potential states which represent a prototype of two-dimensional electronic surface states. Electrons in these states are bound perpendicular to the metal surface by the Coulombic image potential whereas they can move almost freely parallel to the surface. For the (n=1) image-potential state of Cu(100) we find a decay time of 10 fs due to electron scattering with steps and surface defects.