Boot up CS:GO and load into the main menu. If you got into the CS2 beta test, you'll see a popup telling you so (or else a notification in your left-hand main menu bar with a message about the beta). Just click “Enroll” on the popup, and you're good to go! You may need to restart CS:GO to play the beta.

To be eligible for a CS2 Limited Test invite players must have CS:GO Prime status, an active official competitive matchmaking Skill Group, and play majority of their official matchmaking games in one of the regions where the Limited Test is available."

To check if you have access to the Counter Strike 2 beta, open up CS:GO. If you got lucky, you'll see an invitation notification on the main menu. Select "Enroll" on the notification, and then start your download. Once the download of CS2 has finished, reload CS:GO and select "Limited Test" to play Counter Strike 2.