Prior to today, the process for removing Facebook posts from a friend or page was a chore. You had to tap or click around the often confusing settings found on Facebook, until you wound up at the right spot. And that only covered a single account.
Today Facebook announced it was making the process easier by creating a setting specifically to manage your News Feed.
For on-the-fly unfollowing, you can now click or tap (this works on both the website and mobile apps) the small arrow in the top-right corner of a post. According to Facebook's announcement, the drop-down will have an option to "see less" from the person or page, accompanied by an option to Unfollow. However, in both the iOS and Android versions of the app, I'm only seeing the option to unfollow a person. Your experience may vary during the feature's rollout, said to be happening throughout the day.
Where the new feature truly shines is in its full-fledged News Feed management system. You can navigate to it on either iOS or Android by tapping on the More icon, then scrolling to the bottom of the page and selecting News Feed Settings or Manage News Feed (for some reason iOS shows manage, while Android shows the former) from the list.
Three categories are currently present: Friends, Pages and Groups. Scroll through or search any of the lists to unfollow accounts by tapping on the blue Following button. Don't worry, this doesn't mean you're unfriending or unliking the page. But going forward you will no longer see any posts from person or page in your News Feed. Which is good news, if your feed looks like mine on any given gym day.
If you're struck with guilt for unfollowing Mom or a close friend who happens to be super-annoying on Facebook, you can always come back to the same settings section and refollow him or her.