The first, and probably still best, book I read about how our media regularly constructs and perpetuates utter horeshit was Susan Faludi's Backlash.
While about 16 years old now, I guarantee it isn't dated in the slightest. In fact many members of the wacky cast of characters you're very familiar with today were around back then, and Faludi does a good job eviscerating them and the mainstream media. And, not much has changed since then except maybe the horseshit production factory has gotten more explicitly partisan/political.
One of the major examples of horseshit was an utterly unsupport Newsweek article about the chances for older women to get married which included the claim that after a certain age you had more chance of being killed by a terrorist than getting married. Of coure the chance of getting married was pulled out of their asses. The chance of getting killed by a terrorist was pulled out of their asses. The entire thing was pulled out of their asses.
So, it's nice to see that decades later, Newsweek has finally decided to address the fact that they were, in fact, completely full of shit.
My short reading list, in rough chronological order (of relevance not publication), to have a good sense of what's going on in the media (and its intersection with politics) in this country would be:
On Bended Knee
Backlash
Sound and Fury
Queer in America
Fools for Scandal
Hunting of the President
Blinded by the Right
A Vast Conspiracy
One Scandalous Story
What Liberal Media
Republican Noise Machine
Attack Poodles
Lapdogs
...I added a few after being reminded of them in comments. Also, Joan Didion's Political Fictions has been recommended by just about everyone I tend to trust on these things at one point or another. I've never read it, but add it to the list as well.