The radiator is nothing more than a large heat exchanger. It is mounted so that the airflow at the front of the vehicle is forced through the fins of the unit, carrying heat away from the engine coolant flowing through the unit. The fan(s) supplement the airflow by drawing in cool air, thus providing cooling even when the vehicle is not moving.
Because of the need for good air flow, modern radiators and the fans have shrouding or ducting to guide the air through the fins. This duct work, including undervehicle covers and shields, must be in place for proper cooling. Leaving the shrouds and covers off can reduce cooling efficiency and reduce driveability.
Periodically, check the radiator surfaces for blockage by leaves, insects, or mud. Most debris can be removed by hand, and the force of a water hose can be useful in dislodging other items. When cleaning the radiator fins, don't use anything metallic or sharp; the fins are very thin and are easily bent or punctured. Generally, the only times a radiator must be removed are either for repair of a leak or to allow access to other components.
It should be noted that most radiators are mounted to rubber bushings rather than directly to the bodywork. This allows the unit to serve as a vibration damper while the engine is running. The mounts and bushings must be properly reinstalled. Replace the rubber bushings if they show signs of wear or lack of flexibility.