(Before I continue, I'm going to note that this post is a work in progress and will likely be revised. I'll note revisions in bold text at the top of this post.)
Now, there's nothing wrong with a good dose of healthy skepticism, and that's what you need to determine whether or not a story is fake. How do you do this? First, you have to put aside your bias. That's not easy. You may be convinced Obama is a Kenyan Muslim agent or that Trump is the Antichrist, but you have to dig and determine facts. Screw that "facts have a liberal bias" argument. Facts can be proven. They may be uncomfortable. They may go against the grain of everything you believe, but the point is to dig beyond the headlines and the memes to discover the truth.
My definition of fake news is something that is made up out of whole cloth, but is crafted to appeal to a certain segment of the population.
How can you tell? One clue is that the links in the story go back to other stories on the same web site. That's not always a clue for fake news. There could be an "as we previously reported..." link. So follow the links. Do they go elsewhere? Does the link that goes to previous reporting link to the outside world? If so, does the linked story support the article?
Search engines are your friend. Find out what other news outlets are saying. If Fox and CNN and MSNBC and Reuters and the AP are saying the same thing, that's a pretty good indication that the story isn't made up. Look for video, if it exists. There are enough clips and full versions of the recent Trump press conference that you can see and hear what went on - and look out for suspicious edits.
Wait a minute. This sounds an awful lot like the basic research techniques we were taught in school. That's because those techniques still hold up even in this age of technology.
The close cousin to fake news is the story that pulls out one or two bits of truth and builds up a false narrative. Say you run across an article that presents as fact that lungfish can breathe air, so that's proof that all fish can breathe air. All those other species are just hanging out in the water for some nefarious reason that has to do with the conspiracy theory du jour. How do you correct that? Research. Science! I don't suggest you take one of your tropical fish out of the tank and watch it die, because there are plenty of sources to confirm that most species of fish breathe water through their gills. (Yep, I'm being a little simplistic, but you get the idea.)
Then there's misleading headlines, or clickbait. Case in point would be the many articles I've seen shared in the last two days that Republicans have killed the ACA. Buried in those articles is the truth that they voted on a budget resolution that will open the door to to repeal. But the fact is that there are still several steps to go, and your birth control is not going to get more expensive tomorrow. Make no mistake, it could very well happen. (Please don't argue nuance with me. In the end this may be the thing that ultimately does lead to repeal of the ACA, but as of the time I type these words it hasn't happened. I'm not sure enough of our representatives will grow a pair and realize what they're doing, but since that possibility still exits, the ACA may have been coughing up blood last night, but it's not dead yet.)
Then there's satire. Sometimes that can be hard to detect without a label, which you'll find on most satire sites.
What's not fake news: An article that presents a fact that disagrees with your worldview, if that fact can be readily sourced and proven. Example: Some people are calling the fact that John McCain turned the "showergate memos" over to the FBI fake news. Nope. It's a fact that he did that. He said so himself. And I'm going to let you vet that on your own. Now those memos may turn out to be fake. But the fact is that they exist.
(My personal opinion is, while I'm experiencing some schadenfreude over this, in the end I hope they're fake because it scares the you-know-what out of me that a foreign power has blackmail goods on the president, or the man about to assume that office. However, we won't know until they're thoroughly investigated. That needs to happen.)
In conclusion, check sources. Check them again. Don't spread stories and memes without checking them first. Do not make me deploy the Laughing Cat of Shame on you.