Install the watchOS 9 Beta Software Profile
From the iPhone paired to your Apple Watch, go to BetaProfiles.com to download the configuration profile. Your iPhone will notify you when the profile has been downloaded. Go to Settings > General > Profiles & Device Management, tap the profile and then tap "Install" and follow the onscreen instructions.
Update your Apple Watch
Your Apple Watch will automatically receive the latest beta software if you have Automatic Updates turned on in the Software Update settings. To manually check for updates, go to the Apple Watch app on your paired iPhone, tap the My Watch tab, then go to General > Software Update.
You can always delete this installed profile anytime you want to stop receiving beta updates. All you need to do is go through the Delete Profile page, which has all the instructions for each of your devices.
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.