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This DIY found via the internet:

Things You'll Need:
Five gallons of coolant
Crescent wrench
Distilled water
Bucket

1
Move the truck to a level surface to make flushing the radiator easier. Be sure to set the parking brake before beginning any work on the truck.

2
Open the hood of the truck and feel the outer temperature of the radiator. Wait until the radiator is cool to the touch before you remove the cap.

3
Remove the radiator cap once it's cool to the touch. Twist the cap one full turn to relieve any leftover pressure, wait a few seconds and then fully remove the radiator cap.

4
Position a bucket or tray directly underneath the radiator drain on the underside of the radiator. The drain plug should be on the driver's side on a Ram. Once in position, use a crescent wrench to remove the drain plug. Allow all of the existing coolant to drain from the radiator.

5
Take the drained coolant and pour it into a sealable container for proper disposal. Coolant is extremely toxic to people and pets. Take the old coolant to a toxic disposal company or your local auto store.

6
Close the drain plug and pour distilled water into the radiator. Then, open the drain plug and let the water drain back out. Repeat this procedure of filling and draining the radiator until it runs debris-free out the drain plug. It will take approximately 3 gallons of distilled water to complete the flush.

7
Replace the drain plug on the underneath of the radiator. Then fill the radiator with coolant to within 1 inch of the top lip of the radiator.

8
Leave the radiator cap off and start the truck. Allow the truck to run until the cooling fan turns on two separate times.

9
Turn off the engine and recheck the radiator level. If fluid level went down, add more coolant to the radiator. In all, you will need approximately 5 gallons of coolant for the Dodge Ram radiator.

10
Put the cap back on the radiator, clean up debris and close the hood of the truck.