Once the proper configuration profile has been installed from the Apple Developer Center, the new watchOS beta can be downloaded through the dedicated Apple Watch app on the iPhone by going to General -> Software update.
To install the update, the Apple Watch needs to have at least 50 percent battery, it must be placed on the charger, and it has to be in range of the iPhone.
It's not yet clear what features will be introduced in the watchOS 5.1 update, but it could bring support for answering Group FaceTime calls, a feature that was removed during the beta testing period. New emojis are also an option.
We'll update this post when we find out what's new in the watchOS 5.1 update.