This is a good primer, provided by the fact checker at the Washington Post.
The article has great tips, like...
*Determine whether the article is from a legitimate website
*Check the ‘contact us’ page (if there's none listed, it's fake)
*Examine the byline of the reporter and see whether it makes sense (fake news reporters have very fake sounding bios)
*Read the article closely (especially the quotes, if there are any)
*Scrutinize the sources (a tweet is not a source)
*Look at the ads (Naughty Walmart pictures?)
*Use search engines to double-check (Google will usually show you a story is nonsense in the few links)
I would add these two rules...
If it sounds to good to be true, it is. If it sounds like it's written by someone who is telling you exactly what you want to hear, it is.