Don't fear the water: Clean gunk out of Apple Watch under the faucet
If the dial on your watch stops turning smoothly, Apple recommends a dose of warm tap water to get the crown back in working order. Don't dunk the whole watch in water, though. Turn off the device, remove the charger, and detach the leather band before getting it anywhere near your sink. Hold the Digital Crown under your faucet for 10 to 15 seconds and then start turning and pressing the dial to clear the gap between the crown and the case. You shouldn't use soap or any other cleaning products on the watch--just water should suffice.
Once you dry it off, make sure the crown is turning smoothly. If it is but nothing appears on the screen, try a force restart by pressing the side button and crown at the same time for 10 seconds. If that doesn't work, a trip to the Genius Bar may be in order.
For less serious cleaning, a lint-free cloth is the way to go. Stainless steel models with link bracelets and all Watch Edition models come with such a cloth, but Sport owners will have to buy their own.
We already knew Apple Watch was water resistant (not waterproof), but I was hesitant to even wash dishes with the watch on my wrist until Apple published these latest support documents. Now that I know the Digital Crown can survive an encounter with running water, I'm a little less worried--though I'm not sure I'll be brave enough to shower with the watch on like Apple CEO Tim Cook reportedly does.