I can tell you what I do:
1. I don't consume any news from televised sources,
2. I read Foreign Policy, Wall Street Journal, New York Times, The Economist and Foreign Affairs,
3. I'm generally skeptical of everything I read and I try to assume every article's author has many unknown unknowns in their reporting (to counter Gelman Amnesia),
4. Every so often (once a week or so), I read something from a news source I actively distrust just to see what else a nontrivial portion of the population believes about the world.
This isn't perfect, but if you have the free time to do that much reading I think it gets you pretty close to well-rounded. I think the only major way to improve upon this would be to add another major news source from another country for additional foreign perspective (this is why I like The Economist and Financial Times).