When the electromagnetic radiation wave hits the moving object, it "bounces" back toward the source, which also contains a receiver as well as the original transmitter. However, since the wave reflected off of the moving object, the wave is shifted as outlined by the relativistic Doppler effect.
Since the electromagnetic radiation was at a precise frequency when sent out and is at a new frequency upon its return, this can be used to calculate the velocity, v, of the target (which acts as a intermediary source).
Source:
http://physics.about.com/od/physicsintherealworld/f/dopplerradar.htm