On the publication detail page (e.g. https://publons.com/p/1) you will see a “Followers on Publons” section.  If you are not following the paper and are logged in you will see a “+” button in that section.  Clicking that button will add the publication to your followed publications.

You can unfollow a publication from the Followed publications page of your private dashboard or by clicking your profile picture in the “Followers on Publons” section of that publications detail page.