Check the account history of the source. Two red flags are: the number of posts and how long the account has been active. If it claims to be a well know source(like CNN or CBS) and only has a few posts in its history that is a clue. If it's a well know source and the account has only been active a short time that is another red flag.
Images of an event are often reused to deceive people. You can check if an image has been used before on a reverse image search service like TinEye.
Fake news stories abound on Facebook. Most of the postings are produced by scammers looking to make money on the number of clicks these stories receive.
Mark Zuckerberg, the founder and CEO of Facebook, says they are working on a way to weed out these stories. In the meantimes, some creative people have come up with solutions of their own.
The Washington Post ran a story at this link on November 11, 2016 about a group of college students who developed an algorithm that authenticates what is real and what is fake on Facebook.
A programmer named Daniel Sieradski has developed a Chrome extension called the B.S.Detector. Read about this hoax detector at this link.