Sign in to the Apple Developer Center
Sign in to developer.apple.com/account using your Apple ID. You don't need to join Apple's Developer Program, no payment is required, just sign in.
Enable beta updates
On your iPhone paired with your Apple Watch, open the Watch app, go to General > Software Update > Beta Updates, and then choose watchOS 10 Developer Beta.
If you don't see the Beta Updates option, please wait for a while or try again at a different time.
You can always switch to the "Off" option in the Beta Updates to stop receiving future watchOS 10.4 beta updates.
As mentioned, Apple currently doesn't allow watchOS downgrades, so if you delete your watchOS beta profile, you will no longer receive any other beta updates until Apple officially releases them.
Once the beta is installed, it will come with a built-in Feedback Assistant app, which can be launched from the second page of your Home screen. When you come across an issue that needs addressing, send your feedback to Apple with Feedback Assistant.