2 possibilities :
-You've purchased X-plane from Laminar Research directly (on x-plane.com) :
Run the installer to update X-plane and you'll find the beta box to be ticked while going through the update process.
The installer can be found here :
http://www.x-plane.com/kb/digital-download-install/
-You've purchased X-plane from Steam :
Launch Steam and in your games library, right click on x-plane, click on properties. In the subwindow that pops up, under the appropriate tab, activate beta updates. Note that not all beta versions are published for steam users, and that there is some delay (several days) between beta anouncements (
https://developer.x-plane.com) and Steam access to beta.
Hope this helps.