Water resistance

Genius Bar appointment - Unfortunately Apple has made this tricky to get to directly. Go to https://www.apple.com/retail/geniusbar/ > Get hardware help. Select your hardware and continue selecting options requiring replacing parts until you see "Bring in for Repair" --> Sign in with Apple ID

It should turn on automatically as soon as it detects water. Did you turn your crown in an upward motion to expel the water? Have you tried charging it? If the watch is totally non-responsive a trip to the Genius Bar is in order as recommended by Limnos.

Apple has not made it tricky at all. Quite the contrary. Download the Apple Support app. It's wonderful. Sign in with your Apple ID. In this app, you'll see all of your devices by tapping on 'support' at the bottom middle of the screen. Just tap on your device and you'll have a choice of topics. Tap on the topic of your choice and from there you can choose to schedule an appointment or receive a callback to troubleshoot over the phone.

You don’t say which model of Watch you have.