Electromagnetic radiation is produced whenever a charged particle, such as an electron, changes its velocity. The energy of the electromagnetic radiation thus produced comes from the charged particle and its therefore lost by it. A common example of this phenomenon is the oscillating charge or current in a radio antenna. The antenna of a radio transmitter is part of an electric resonance circuit in which the charge is made to oscillate at a desired frequency. An electromagnetic wave so generated can be received by a similar antenna connected to an oscillating electric circuit in the tuner that is tuned to that same frequency. The electromagnetic wave in turn produces an oscillating motion of charge in the receiving antenna. In general, one can say that any system which emits electromagnetic radiation of a given frequency can absorb radiation of the same frequency.
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).
The Doppler effect
When the source of the waves is moving toward the observer, each successive wave crest is emitted from a position closer to the observer than the previous wave. Therefore each wave takes slightly less time to reach the observer than the previous wave. Therefore the time between the arrival of successive wave crests at the observer is reduced, causing an increase in the frequency. While they are travelling, the distance between successive wave fronts is reduced; so the waves "bunch together". Conversely, if the source of waves is moving away from the observer, each wave is emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is increased, reducing the frequency. The distance between successive wave fronts is increased, so the waves "spread out".
Source:
http://physics.about.com/od/physicsintherealworld/f/dopplerradar.htm
http://www.britannica.com/EBchecked/topic/183228/electromagnetic-radiation
http://en.wikipedia.org/wiki/Doppler_effect
http://upload.wikimedia.org/wikipedia/commons/7/7f/Doppler_effect_diagrammatic.svg