If you haven’t done so yet, head over to our WoW Classic website and select the opt-in button to become a beta tester.
Players who have opted-in can be selected to be a tester, and invitations will go out regularly throughout the test.
Once you’ve been added:

Open the Blizzard Battle.net App and select World of Warcraft from your Games list.
In the selector above the Play button, change your Game Version to In Development: Cataclysm Classic Beta.
Click Install to install the Beta client. This becomes a Play button when ready.
Click Play to log in to the Beta, and select any of the available Test Servers.
Create a new test character (or when available, copy over a character from your live WoW Classic account using the Copy Character button), then enter the game and test the content!

If you have issues installing and operating the Cataclysm Classic beta, please first check our Common Technical Issues and Solutions to begin troubleshooting.