Having journalistic standards that were enforced by Law.
It's a can of worms, especially in a country that is as suspicious of it's government as America, but in my view, one of the biggest changes in people's views of the media (and "truth" in general) is the steady erosion of Journalistic standards - putting infotainment shows and opinion pieces on the same level of journalistic rigour as actually well written, high standard news stories.
News corps will continue to chase money, and money is tied to viewership - which gains from people being engaged through polarising, emotion driven content.
If there are no standards for this kind of thing, people will gravitate towards the stuff that gives you that hit of emotion, and they'll forgo and bend facts to present a story in a way that keeps their viewers at the expense of fair representation of facts, and bias.
In the context of social media, it's tricky, because robo websites and opinion pieces run rife through them, with pieces debunking them and/or apologising for incorrect facts not propogating as hard - so in my view there needs to be some level of targeted/intelligent regulation of social media as a news source. (Content aggregators perhaps taking some level of responsibility of curating what is being shared? Admittedly difficult to do this without getting Orwellian...)
But that's just my opinion, interested to hear if people think it's a load of BS or not.