You've probably seen plenty of articles that sound something like "Lorde Gives Anti-Capitalist Speech at the Grammy's", "How GMOs are Doing _____ and We're All Going to Die", or "Something Nuclear Happened and We're All Going to Die." And while some of them are at least partially true (for instance, nuclear particles from the Fukushima meltdown are supposed to hit the west coast by, well, now and allegedly it won't have any negative impacts on humans or sea life, but maybe stay out of the water just in case?) a lot of them are exaggerated, misinterpreted, and sometimes straight-up fear mongering. Some articles are easy to disprove-- the Lorde example, for instance, was posted on a parody news website-- but when it comes to science-related things, it can be hard to tell what's correct if you yourself are not really scientifically (or statistically) educated. I'm obviously no expert, but here's what I look for when I try to fact check things beyond my scope of understanding:
Check the sources, author, research, etc. If the news comes from a website called something to the effect of "The Daily Sheeple", "Only Organic Foods", or anything referencing conservativism or liberalism, it's probably a biased, unreliable source. If the article got its information from something that has very little to do with what they're writing about, it's probably inaccurate. If the author is writing about the effects of nuclear waste but they're a nutritionist rather than a nuclear scientist (which has actually happened when I tried to fact check something), they probably can't be trusted to write about it accurately. And so on.
Google it. Not that this necessarily yields better sources, but I've found that a lot of scare articles were written based on misunderstandings or exaggerations by googling things. Or I've found mainstream news articles (which aren't necessarily much better) addressing the same subject and alleging to have consulted actual experts on whatever topic, which suggests that their story may be more accurate. If nothing else, googling certain headlines allows you to see what kind of news outlets are reporting the story-- and, if a majority of them are from places like The Daily Sheeple, you pretty much have your answer.
Snopes. I actually doubt that Snopes is the best way to fact check things, but generally Snopes gives you a definitive answer with lots of reasoning and sources. So you can always just fact check the fact checking.
Check the chart. There are a whole bunch of scientific/statistic procedures that may be completely meaningless to you if you haven't studied either subject in much depth, but the gist is that these procedures have a HUGE impact on the results. So, if they're not followed correctly, the results could very well be inaccurate. For the sake of convenience, I found a chart that pretty much outlines them.