Mark pretty well covered it, just be sure you followed the book about reving the engine to clear the air out of the system, I ran mine at 3000 for about 5 minutes and it blew all kinds of air out before it finally settled down. Once it stopped I tightened the cap and haven't had a problem since.
Sorry to hear that the water pumps tend to fail, even slowely. I'm probably going to regret not putting a coolant filter on one of these days.
I'm changing coolant every 3 years regardless of mileage and using distilled water. Maybe it will last a little longer that way.
02 2500HD LT D/A SB CC 4X4 BLACK, Westin stainless nerf bars, BW GN Hitch,Racor 60S post oem fuel filter, Oil Guard bypass engine oil Filter. All synthetic fluids. Kennedy boost valve, edge, Modified air intake,EGT & Boost digital gauge,TransferFlow combo fuel & tool box, Air Lift Suspesion Bags Rear & compressor with remote, Bilsteins front & rear, Frontier front replacement bumper.