To get Yahoo Mail Beta, just switch your content preference to Germany, France or UK. Then you will be asked if you want to join the beta when you log into your Yahoo Mail. Say yes, and join the beta. Then from the options menu, change your content preference what it was before. Then go to Yahoo Mail again. You should see Yahoo Beta. If you don't see it, go to options and click "Try Beta" button. That's all.
How to change your content preference:
* log in to Yahoo Mail
* click Options
* select Account information from the left panel
* go to Member Information, General Preferences, Preferred Content
* select, for example, Yahoo UK
* click Finished
* go to Yahoo Mail
* you'll see a page that says "It's the New Yahoo! Mail Beta... and you're invited."
* click on "Try Beta Now".
Related:
Yahoo Mail has unlimited storage
Yahoo Mail Beta vs Gmail
Update [September 16]: Now you can get Yahoo Mail Beta from this page.