As a practical matter, I think the only thing a person can do is consciously seek out both sides of the story. Read a credible conservative daily (WSJ, Chicago Tribune) and a left-leaning Sunday paper (WaPo/NYT)/news magazine. Get both sides of the issue and see which you find more persuasive.
The fact that either the Washington Post or the New York Times is considered left-leaning is one of the problems in US media. They are both corporate rags pushing the neo-liberal plutocrat agenda. Try Jacobin or the London Review of Books as a somewhat left of center starters.
The above description of the NYT, however, is (a) not only a conservative's idea of what an opposing partisan newspaper would look like, it's almost a parody of such an idea (b) only sustainable through the lens of confirmation bias.
It's a huge difference. In one case you have a system meant to deliver information to inform, and which can be criticized if it fails to do so, which it often (or even mostly) failed at. Then there is these new media sources of 'information', which are not even trying, and nobody expects to try. One is a subversion of the standards which are explicitly expected, and the other is a system that has no standards whatsoever.
This is part of the myth making that took hold after the New Deal, when the Establishment decided how things were going to be and made it so. If you have licensing powers over broadcast media you can use this to ensure that discussion stays inside the bounds of discourse you deem acceptable. Because these local media companies often had both broadcast and publishing arms they had a strong incentive not to piss off the regulators who could take away their broadcasting licenses.
This long period of manufactured consent lasted until the people who realised it was artificial retired or died and then technology allowed more diversity of opinion. Cable and talk radio allowed many, many more voices to be heard and expanded the Overton window, bringing the US back to normal politics where people really, really hate each other unless there’s an external enemy to hate more.
In the immediate post colonial period Aaron Burr killed Hamilton in a duel. In 1856 Preston Brooks beat Charles Sumner with a cane on the floor of Congress. Andrew Jackson was held in much the same esteem by large swathes of the US population as Trump is now. In the 1960s there were over 3,000 domestic bombings and riots and demonstrations aplenty.
The media being hyper partisan is not new. What’s new is how obvious it is. It took decades for Walter Duranty’s lies about the Holodmor, the Ukrainian Holocaust to be exposed, and the Pulitzer Prize Committee still hasn’t revoked it. This for a cover up of millions of deaths in the pages of the NYT.
The prestige press is no more unbiased than Mother Jones or Breitbart.
https://deadline.com/2016/11/shocked-by-trump-new-york-times...
> For starters, it’s important to accept that the New York Times has always — or at least for many decades — been a far more editor-driven, and self-conscious, publication than many of those with which it competes. Historically, the Los Angeles Times, where I worked twice, for instance, was a reporter-driven, bottom-up newspaper. Most editors wanted to know, every day, before the first morning meeting: “What are you hearing? What have you got?”
> It was a shock on arriving at the New York Times in 2004, as the paper’s movie editor, to realize that its editorial dynamic was essentially the reverse. By and large, talented reporters scrambled to match stories with what internally was often called “the narrative.” We were occasionally asked to map a narrative for our various beats a year in advance, square the plan with editors, then generate stories that fit the pre-designated line.