Police radar guns work by virtue of the Doppler Effect.
The doppler effect is essentially: consider a stationary source of electromagnetic radiation. In 3D, the spherical wavefronts emanate from the source (sort of looks like the target symbol). However if the source begins to move in a certain direction, it moves towards the wavefronts that it emits in that specific direction and so the wavefronts emitted by the source as it moves are compressed in the direction of motion and rarified in the opposite direction. So in the direction of the motion the frequency of the emitted radiation increases and vice verse for the opposite direction.
The radar guns basically work using some sort of electromagnetic radiation (I think they use lasers now). We know, v=f*lambda, so an increase (if source is approaching observer) or decrease (if source is receding from observer) in the frequency of the signal returned to the radar gun is proportional to the source's (possible offending driver's car) speed of approach/departure and you can book the driver etc if exceeding the speed limit.
