Samsung recently announced the One UI Watch beta programme for the Galaxy Watch4 and Galaxy Watch4 Classic, and it is now available in the United States for both smartwatches.
Those interested can join the beta programme through the Samsung Members app, which will have a banner at the top that says "One UI Watch Beta Program." To apply for the beta programme, click on it and follow the instructions. You will be registered in the beta programme if you meet the participation requirements.
You can download the One UI Watch beta on your Galaxy Watch4/Watch4 Classic once you've completed the enrollment process. However, it will not be possible before June 2, as Samsung will begin distributing beta versions on Thursday. Furthermore, the beta programme is only limited to Samsung smartphone owners, meaning non-Samsung smartphone owners will be unable to participate at this time.
It's also worth noting that the One UI Watch beta programme isn't accessible for Galaxy Watch4/Watch4 Classic special editions (save the Gold edition) or other models. You won't be able to join the beta programme again if you leave. It is also not possible to revert to a previous software version.