Getting a discussion tab on a github repository?

If you're looking for per-repository discussions like in the link you mentioned, that's a new feature that is in a limited beta at GitHub. It will be rolling out to more repositories and projects soon and GitHub will provide more information when it's available more widely.

Update Dec 2020

You can enable it from project settings.

Old Answer:

As of Oct 2020, private repositories are not eligible for the Discussions beta.
Repos must:

  1. Be public visibility
  2. Have at least 3 contributors


As of the 9th of December Discussion tabs are now rolling out to all GitHub’s repos just go to settings to were you can turn off and on; issues and wikis etc, at end you will see the new discussion tab option view a screen shot