1. Check the domain or URL: News organizations usually have a pretty clear domain and brand. Usually, these end with ".com". Be wary of sites that end with .co or another uncommon domain.
2. Check out the "About Us" section on unfamiliar websites. Some websites are satire, or meant to be a parody of the news. The Onion and Clickhole are good examples.
3. Are there quotes from respected sources or individuals in the field?
4. Reverse image search: right click on the image and click on "search Google for the image". If the image is at all related to the story it will come up in Google as will other sources who are reporting about it.
5. Check the date: some stories are not fake, but republished to distort what is going on in the current news.
6. Research the author: click on or Google on their name to see if they are really a known or respected writer.
7. Can you find this story anywhere else? Once news is picked up it spreads pretty rapidly, so more then one news outlet should be reporting it.