Connect your iPhone to your computer with the USB cable it came with. Xcode communicates with Apple Watch wirelessly via the iPhone. Xcode will download the watchOS device symbols from server and then after a few minutes your watch should be an available device in the Run Destination pop-up. (If you are using a Personal Team for signing you will need to trust it before the app will run on the device.)
I have an identical issue to the author and I can't really run still. I can see "Apple Watch via iPhone" as a destination but it doesn't run. Xcode reports:
The run destination Shibo's iPhone is not valid for Running the scheme 'lemonwatch WatchKit App'.
There was an error preparing Shibo's Apple Watch for development. Try reattaching the device to which Shibo's Apple Watch is paired. Xcode encountered an error
After I unpair my iPhone from Devices and Simulators window, reconnect it and run, Xcode sometimes would just run and reports "Running xxx on Apple Watch" but soon reports:
Failed to use existing instance 0 for app with bundle identifier: com.apple.Carousel
macOS Catalina 10.15(19A602) - MacBook Pro (Retina, 15-inch, Late 2013)
iOS 13.1.3(17A878) - iPhone 11 A2223
watchOS 6.0.1(17R604) - Apple Watch Series 5 44mm A2157
Xcode Version 11.1 (11A1027)
I have a similar issue where I have successfully install the app on my watch before, but there are other times when I compile it doesn't transfer the app to my watch. Xcode behaves so inconsistently. Has anyone figured out how to make sure it always gets intalled on your watch?