We present a circuit model to describe the electron transport through a domain wall in a ferromagnetic nanowire. The domain wall is treated as a coherent four-terminal device with incoming and outgoing channels of spin up and down and the spin-dependent scattering in the vicinity of the wall is modeled using classical resistances. We derive the conductance of the circuit in terms of general conductance parameters for a domain wall. We then calculate these conductance parameters for the case of ballistic transport through the domain wall, and obtain a simple formula for the domain wall magnetoresistance, which gives a result consistent with recent experiments. The spin transfer torque exerted on a domain wall by a spin-polarized current is calculated using the circuit model, and an estimate of the speed of the resulting wall motion is made.