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You can think of a radar unit as a flash light. Instead of emitting visible light, radar emits invisible electromagnetic waves at a certain frequency. When you shine a light beam from a flash light over an object, the light is reflected back to your eyes so that you can see the object. The same principle applies to radar beams. The electromagnetic wave that radar emits is called microwave, which will reflect off most metallic objects, concrete, trees, wood etc. It will however go through grass, bushes etc, just like light will go though glass and transparent objects.
The radar unit uses an antenna to "read" the microwave that is reflected back from an object (such as a car), just like you use your eyes to capture the reflected light from your flash light. If the microwave from the radar hits a moving target, the waves' frequency will change based on the "doppler shift" principle. With the reflected wave's changed frequency, and the known frequency that the radar emits, the computer inside the radar unit will be able to calculate the target speed. Note that radar cannot determine the target speed when the target is travelling perpendicular to the radar beam, since there will be no doppler shift relative to the radar antenna.
It's that simple. However, you might be already aware, that there are so many shortcomings to traffic radar. First of all, radar is prone to interference. It is not too hard to figure out that the radar's antenna will accept any microwave that it is able to "hear". In other words, the antenna might not be "hearing" the waves which originated from its own unit. High voltage power lines, telephone lines, power stations, even neon lights, do emit lots of electrmagnetic waves. There is absolutely no way to tell which wave the antenna is hearing. Secondly, radar cannot determine which target reflected off the waves. If there are two cars both travelling in a close proximity, no one can tell who is responsible for the radar reading if such is obtained. Identifying the target is a job left to the radar operator, who frequently makes mistakes. At a distance of 200m, the width of the radar beam can usually cover all 4 lanes of traffic travelling in both direction. In other words, it is impossible for the cop to know exactly which vehicle is responsible for the radar reading he obtained, even if there is only one vehicle on the road he can see. The reason is radar has a typical range of approximately 400m (1200 feet), which is beyond the visual range of most human eyes. The radar might be clocking a speeder at a distance of 300m, but the cop can only see an innocent driver coming towards him at a distance of 100m. As a result, an unjust ticket will be issued. Not to mention if there are more than two cars in the visual range of the cop.
Furthermore, radar does not necessarily pick up the fastest moving object. The strongest return signal can be affected by a number of different factors, such as the target's size, the cross-sectional area facing the radar antenna, its relative speed and the distance from the radar unit. For example, if a Corvette is travelling at 80km/h 50m from the radar, and a truck is speeding 110km/h at 200m away, the radar may pick up the return signal from the truck and register a speed of 110km/h. The officer however might think that the Corvette is the one responsible for the violation and therefore issues an undeserved ticket. In addition, when traffic radar is used near an international airport, the radar will pick up the return signals from airborne objects. In this case, extremely fast speeds such as 300-400km/h will be registered on the radar. Even if an aircraft is flying at a few km's away, the radar will still be capable to pick up the return signal since an aircraft is much greater in size and has much faster speed than any ground vehicle. I can't imagine if you are being charged 300km/h in a 60km/h zone by a clueless cop.
Of course, there are radar units which can identify multiple targets, determine their speeds, range, shape, altitude, direction of travel etc., but these radar units cost millions of dollars and are properties of the military and airports. Traffic radar units have to be cheap, small, and thus error-prone.
There is a variation of traffic radar, which is called moving radar. It works pretty much the same way as the type described above (stationary radar), only that moving radar is used when the cop car is moving (for the purpose of highway patrol, for example). There are two readouts on the radar unit, one shows the target speed, one shows the cop car speed. The strongest return signal, usually reflected from highway signs, bridges or other objects, is assumed to be the cop car speed. The next strongest signal, is assumed to be from the target. Since the target speed will only be relative to the cop car speed, therefore by adding the cop car speed to the relative target speed, one will get the absolute speed of the target. Moving radar is subject to all the errors stationary radar has, plus the error of determining the cop car speed.
There is another type of traffic radar, which is photo radar. It was used for a short time in Ontario, then slashed when the new Government took over. However, photo radar is used in many other provinces and in the States. Strictly speaking, photo radar is not a variation of traditional radar. It is basically a stationary radar with the capability of taking photos. Photo radar is never used in moving mode. A police officer often sets up the photo radar on the shoulder of a highway, pointing the radar towards oncoming traffic. For stealth reasons, the radar unit is hidden in a vehicle, usually a minivan. There will be a camera mounted on top of the vehicle, connected to the radar unit. After the photo radar unit is set up, the police officer can go to sleep, read the paper, or eat donut. The radar will monitor traffic speed continuously, if a violation speed above the threshold speed is detected, the camera will automatically take a picture of the violating vehicle's license plate. At the end of the day, all the pictures will be developed, and a ticket will be mailed to the respective registered owners of the vehicles.
Radar is not infallible as most people and courts believe. Although the technology has advanced a lot during the years, and the radar units have become more and more user friendly, it doesn't change the fact that radar still makes mistakes especially at the hands of a poorly trained operator. I have received emails from police officers and provincial prosecutors who read this page, telling me that today's radar units no longer need any calibration. All they need to do is to push a test button on the unit. If the unit says pass then the radar is good, if it says fail then it is bad. This is absolute nonsense. The test button on the radar unit is only a simple check of the unit's internal circuitry. Successfully completing this INTERNAL check says absolutely nothing about how accurately the radar will display speed readings from EXTERNAL inputs. Usually tuning forks are used to perform this external calibration test. Since tuning forks are extremely delicate tools, and they need regular certification, so the prosecution will want to minimize the cost of operating radar units by introducing this blatant nonsense.
Only we get our act together the Government will slash this error-prone technology to enforce traffic speed. Much of the research and development work of radar manufacturers has been concentrated on defeating radar detectors, therefore we can be quite certain that Governments are not really interested in road safety, only money.