This badge is given to users who essentially sign up for the site before the site actually exists. They don't actually sign up at this time, of course, because the site doesn't exist, but following a site during the proposal phase is a statement of intent.
Each site that isn't part of the trilogy (Stack Overflow, Super User, Server Fault) went through a proposal stage on Area 51, where the site was defined and people "followed" it. Once the site gained enough interest, it entered a commitment phase, and once enough people committed, it went into a private beta, followed by a closed beta. Until a site reaches the "beta" phase, it doesn't actually exist.
In order to earn this badge, you must follow the proposal before it enters commitment phase, which is not something you can do on this site now since it has been public for some while.
This entire process is covered in more detail on the Area 51 Frequently Asked Questions Page.
In short: You can no longer earn the precognitive badge or beta badge on Ask Ubuntu.