Proceed with draining the system as outlined above. When the system has drained, reconnect any hoses close to the radiator draincock. Move the temperature control for the heater to its hottest position; this allows the heater core to be flushed as well. Using a garden hose or bucket, fill the reservoir and allow the water to run out the engine drain cock. Continue until the water runs clear. Be sure to clean the expansion tank as well.
If the system is badly contaminated with rust or scale, you can use a commercial flushing solution to clean it out. Follow the manufacturer's instructions. Some causes of rust are air in the system, failure to change the coolant regularly, use of excessively hard or soft water, and/or failure to use the correct mix of antifreeze and water.
After the system has been flushed, continue with the refill procedures outlined above. Check the condition of the radiator cap and its gasket, replacing the radiator cap as necessary.