To participate in the WotLK Classic beta, please follow the steps below carefully. This shouldn't take you more than a minute or two:

Click this link to go to the section of the Battle.net website dedicated to Wrath of the Lich King Classic Edition
Log in to your account using the "My Account" drop-down menu in the upper right corner of the page
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Then scroll down the page until you reach the "Register for Beta" section.
Click "Sign Up for Beta"
You should normally sign up for the Wrath of the Lich King Classic Beta!
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There is nothing to do, the rest is automated. If you're lucky, you can get access from the first announcements of the official Wrath of the Lich King classic beta. You can buy wotlk classic gold at that time to gain huge advantages.