Sign up for the betaMany people don't realize that you need to sign up / opt in as interested in playing the beta before you even have a chance of being picked. Without doing this, your chances of getting a key is next to none.
Anyway, log in to your Blizzard Account, then go to "Games & Subscriptions" in the right-hand menu. Scroll to the bottom of this to find the "Go To Beta Profile Settings" button, and click on this. This will take you to a list of all the Blizzard franchises, and World of Warcraft Classic is one of the franchises you can mark yourself as interested in testing.
As you can see from the screenshot above, click the box for World of Warcraft Classic, and you are marked as a potential beta tester.
Doing this far from guarantees you a beta spot, but it's the first step. Most people just do this and wait, and if you are lucky, your account will be flagged to get beta access at one point in the future.
Become a content creator to get a guaranteed spot in the WoW Classic betaRight now it seems like the only way to get a guaranteed invite to the World of Warcraft Classic beta is to be a content creator, which means you must be a streamer, create WoW YouTube videos or something like that.
It's not known exactly how many subscribers or followers you need for Blizzard to send you a beta invite, but it can be very difficult to reach this point in a short amount of time. So this option is rather unlikely unless you already are a content creator. If that's the case, then you should contact Blizzard to get in touch with them about granting you beta access.