
The first Android 10 beta is already rolling out over the air, and once you have registered, you can go into the Software update menu of your Galaxy S10's Settings app and tap Download and install to start downloading the beta software. It may not be immediately available for everyone, and if that's the case, just keep mashing the Download and install button until the update shows up.
The software version for the first beta is G970FXXU3ZSJ8, G973FXXU3ZSJ8, and G975FXXU3ZSJ8 for the S10e, S10, and S10+ respectively. The download size varies by device: 1865 MB for the S10e, 1867 MB for the S10, and 1900 MB for the S10+. Samsung doesn't say anything about registration slots for the beta being limited, but you might want to hurry and register as soon as possible to make sure you don't miss out.