There's no standardized way but there are a few well established ones.
And note that there are two questions in your question. The first is whether a piece of news is factual. The other is whether it's being spun as something it's not.
For the factual bit, a proxy is whether the piece of news got picked up by a well established news outlet. You're familiar with their names already. Think the Wall Street Journal, the Financial Times, the Economist, the New York Times, the New Yorker, the Washington Post, the Boston Globe, the Miami Herald, the Chicago Tribune, the LA Times, the SF Chronicle, Deutsche Welle, Le Monde, and so forth; as well as news agencies like AP, AFP, or Reuters. Pick two or three to be on the safe side and that should help you weed out non-factual stories and possibly true stories of dubious importance.
What these outlets have in common is that they tend to only report what they have fact checked. And when they're unable to fact check they make it explicit by distancing themselves with what's being reported. For instance, for a short while yesterday the Guardian was reporting that US media were reporting that Epstein committed suicide, and this was a clearcut sign that they hadn't fact checked it themselves yet.
Just to be clear, I don't mean here that reading those is a surefire way of never running into "news" stories that turn out false -- sometimes there's a blunder. When there is, you'll find a correction more often than not (except on Bloomberg). But for the most part they do their job properly.
Be wary, as you read those outfits, that opinion pieces are not reporting. And more generally speaking, never read opinion pieces as if they were factual, because more often than not they aren't.
For the spun bit, you're way ahead already if you stuck to the above news outfits and take opinion pieces with a giant fistful of salt. The key here is to understand that there are three types of articles in newspapers: news articles, analysis, and opinion pieces. In general (but not always), news articles are fact based and fact checked. Analysis builds on facts from news articles and spins it. Mind that there's a growing trend to mix analysis directly into news articles. vox.com epitomizes this trend, by literally encouraging their writers to not bother finding some expert for a quote just to spell out the bloody obvious and call a cat a cat. This trend may have contributed to lower trust in journalism; or maybe not -- I honestly don't know. Opinion pieces are, more often than not, spin that is loosely based on facts from news articles -- sometimes it masquerades as trying to connect the dots, sometimes it builds upon an anecdote and turns a molehill into a mountain, and so forth. As a rule you'll do well by not reading the opinion section of most newspapers if you're only interested in what's factual.
When all else fails, there's a number of fact checking websites and media bias references to look into if you really want to double check. Among the notorious fact checking websites: snopes.com, politifact.com, factcheck.org, etc. The two that repeatedly top searches when querying what a news source's bias is are mediabiasfactcheck.com and allsides.com
