How bad is the coolant? If there is a lot of sediments (muddy buildup) then you need to use caution. If there is a lot of sediments, you need to get them out in one pass.
First, drain the radiator. You may want to bypass the heater core because sediments will clog a heater core because they have real small fins and are a PITA to replace. Use the hose and run water throught the lines both ways, this will flush out without the danger of radiator junk clogging it. Then remove the t-stat (this makes it easier, won't have to wait until it heats up) and put the housing back, don't worry if it leaks some on the old gasket, your going to replace anyways when you install the new t-stat. Pull the upper hose. Fill the radiator with water and leave the hose in the radiator while running with the upper hose removed. Start the car and all the water will flush the gunk out. This way no fluid will recycle. When all junk is out, re-attach the upper hose. Add some radiator flush and allow it to run normally, maby take if for a drive. Pull th upper hose, add garden hose again and flush again. Do this until the water comming out looks like the water going in. Drain radiator, install new t-stat, re-attach the heater core, and then fill with coolant.
