it works by convection and radiation.
the energy that is generated by the engine that doesn't go into making the pistons go up and down is heat energy. too much of this is bad for your engine so what you have is a water jacket surrounding the hottest parts of your engine. in this jacket there is water. the heat transfers by conduction into the water and through a process of thermal dynamics and the water pump the hot water is taken from the engine and then goes through the radiator. now comes the really good bit. cold air is forced through the radiator by the movement of the vehicle through the air, there is also a fan used to draw air through the radiator so even when you are not moving you still get air flowing through the radiator.
the radiator has a number of water ways in it and these water ways have fins on them. so with the air rushing past the fins the heat that has conducted itself from the water into the metal of the fins via the radiator core is taken away leaving cooler water to recirulate back to the engine.
there are a number of variation on this simple but effective idea these include but are not limited to electric fans and a smaller radiator in the vehicle cab that can be used as a heater ( except the one in series landrovers)
simple really, i'm surprised you didn't know