Install your new radiator, then run your top radiator hose into a five-gallon bucket. Connect your bottom hose to the radiator. Fill your radiator with water and fire up the engine. When the thermostat opens, hot water will rapidly fill the bucket (keep feeding new water into the radiator). I'd recommend having two buckets, so you can empty one while the other is filling. When the water runs clean, shut off the engine and connect your hose to the radiator. Drain the radiator dry, and then fill it with coolant. You can adjust the mix over a period of a couple of days- draining from the radiator so you can add more coolant, if necessary.
Don't let the critters get to the old coolant, they will drink it!
