This does not mean that fake news items will disappear from your News Feed. Instead, stories that are tagged as fake news will be accompanied by a warning label underneath indicating that it's been "Disputed," along with listing the fact-checkers that deemed the story as fake. Users can hover over and click on the news item to see why it has been tagged as a disputed.article.
The flagging system applies only to individual stories. For example, if a news item is marked as Disputed, only that article will carry the tag rather than the entire source site.
Facebook did not go into great detail about this new system, including how a Disputed tag might affect its ranking algorithm. It's not clear if Disputed stories will show up less frequently than stories without the tag, or if Facebook will leave that aspect alone and count on its tagging system being enough to stop a fake news item from spreading.
This is likely the first step of more to come. Back in November, Stanford posted a study suggesting that students are easily fooled by fake news. The study focused on 7,804 students from middle school through college. Given the influence that fake news can have, and the level of difficulty in discerning real stories from hoaxes, Facebook's work in this regard is far from over.