Radar has many uses, from missile detection to the speed radars, and the principle behind it is actually fairly simple, based on two relatively uncomplicated principles: echoes and the Doppler Effect.
Echoes are the easiest to explain, mostly because it's something that almost everybody has played around with. Sound waves (and light waves) have the property of being able to be reflected off of certain types of surfaces. When you make a sound toward one of those surfaces, you will be able to hear a slightly distorted version of your sound after a time delay. An echo is simply a sound wave being bounced off of a surface.
Next up: the Doppler Effect. The Doppler Effect can be simply stated as the distortion of waves that originated from a moving source. The classic example is that of a moving car blaring it's horn as it moves towards you: as it approaches your position, you hear a high pitched tone, and as it moves away from you, you hear a lower pitched tone. That would be the result of the Doppler Effect. As the car moves toward you, it is pushing the sound waves toward you, resulting in them being "scrunched" up. This changes the wavelength, and thus the frequency, making the horn sound higher pitched than it really is. As the car moves away, you hear the effect of the waves being "stretched" out, resulting in a longer frequency.
Wave Physics
Radar, Part 1
Radar, Part 2
Lidar
Bibliography
Tl;dr