Critical thinking can eliminate a lot of sources, especially if one keeps up with current news. Does the source use unnamed sources too often? Does the story "make sense?" Which political figures does the source follow...which will tell one if they are "left leaning," or "right leaning." If they use about an equal number from both sides of the political spectrum, they may be more balanced than other sources. Do they use a lot of hyperbole, or words that are designed to trigger emotion? If so, they are not likely objective. Reading about the authors of written pieces, getting their biographical information so one knows their background - also helps to understand their perspective and whether or not they are really experts in the field about which they are writing.
I simply "don't do" politics on Facebook. With 2 pages, I use one for family and personal friends - and the other professionally. Politics don't have a place with either group - there is too much room for misinterpretation, so I simply "hide" political messages from my feed. And when listening to sources on television media, I listen carefully to their wording. If I'm skeptical, I'll look it up on-line. I take nothing at face value when it comes to news.