How full of water should the radiator be?

When the engine is cold, the thermostat is completely closed and allows heat to build up in the engine, by allowing water to circulate only through the engine (and the heater core). When the coolant reaches the thermostat's activation temperature, it begins to open, allowing water into the radiator. The thermostat will open as far as needed to maintain the design temperature, by metering the amount of water going to the radiator. How far the thermostat opens depends on many factors, such as engine power (=heat) produced, the air flow through the radiator, outside air temperature. The basic process is entirely mechanical, the only electrically controlled part is the electric cooling fan.