You’ll have to go to first to beta.apple.com and log in with the same Apple ID that you use on your Apple TV. Once you accept the agreement, you can go to your Apple TV -> Settings -> system -> Software updates -> and turn "Get public betas" on.
Once it’s turned on, you can click on the update button and it should offers you the latest tvOS public beta avaible (which is tvOS 12.1 beta 2 for now)