What is the proper way to clean a water heater?
Not sure there's a right way, just people with different preferences. Here's what I think is important:


You need water entering the tank from the cold side, so it should be open for most of the process. The cold line goes to the bottom of the tank, which is where the sediment will be. I personally turn my supply off when first opening my drain in case that valve malfunctions, but I've got a pretty cheap drain valve.
You want as much pressure going through the cold input to kick up the sediment, so try to leave all the valves open as much as possible. If your drain is a little slow, then opening and closing the cold shutoff might be a good way to get more sediment stirred up.
Monitor the discharge. On my next cleaning, I plan to run the hose into the utility sink next to the hot water heater so I can watch the result. Without doing this, you're missing a key piece of data to know when you can stop. I'd run 5 or so gallons after you see it start to run clear.