The procedure I use is as follows:
1. Drain fluid
2. Remove the thermostat
3. Reinstall the t-stat housing and upper radiator hose
4. Disconnect upper radiator hose at radiator
5. Flush system with garden hose through upper radiator hose until water runs clear
6. Disconnect heater hoses, open heat valve
7. Flush heater core
8. Flush overflow tank
9. Drain as much water as possible from cooling system
10. Siphon water from overflow tank
11. Reinstall thermostat
12. Button everything back up
13. Refill cooling system with specified amount of antifreeze, bring up to level with water, preferably distilled
14. Run car, top off coolant
15. Keep adding water as required every morning until system is topped off.
This procedure is done on a cold engine. I use this method for every car I own. Since there is rust in the cooling system of the Taurus, you may want to consider a citric acid flush treatment.
Keep in mind that flushing a neglected cooling system can sometimes dislodge corrosion resulting in a radiator leak. Be prepared for that.