Everyone is biased because everyone has opinions. When news sources present stories that contain their opinions, their reward is making money off it from their target audience, so they continue to do it. But even without the money, people will still spew their opinions about things they feel strongly about, as evidenced by every Facebook comments section ever. It's just part of being human.
However, and I can't emphasize this enough, just because someone is biased doesn't mean they're not telling the truth. No matter what newspaper you read, no matter what some friend or coworker or family member tells you about the news, no matter what you find on the internet, it has a bias. Some of the information you stumble across really might be fake, but it's so dangerous to automatically assume that if something disagrees with you it must be fake. President Trump's pervasive rhetoric about "fake news" is so damaging because it sends the message that just because a source says something you personally don't like, that means they're lying and can never be trusted, and that's just not true. Yes, the New York Times has a bias against Trump—that doesn't mean they make up lies about him, it means that when they report on him they're going to be less forgiving of his mistakes/point out more of his flaws than a source like Fox News would be. Like Guesthouse says below, most sources report the same basic facts, and it's just the added rhetoric they tack onto them that differs.
But what can YOU do to find the truth in a world where everyone is biased? First of all, realize that everyone is biased. Second of all, do what you can to ascertain the reliability of a source—just because everyone is biased doesn't mean that everyone has the same level of reliability (the New York Times, for example, tends to be far more reliable than Breitbart News, even though both of them have a bias). Is it from a reliable network? Do other sources corroborate it? Do they have data or facts to back up their claims? Has Snopes or Politifact either supported or called out their claim? Are they trying to appeal to the worst parts of human nature by relying on things like fearmongering and hatred? (Stories like that are generally less reliable, so beware whenever you see a headline like, "Muslims are destroying America!"). Was whatever you're reading written recently? Is the author somebody who would know what they're talking about? (Most journalists, for example, have a much better grasp on developing news stories than random bloggers do). If you're on the internet, is it coming from a legit URL? Is what they're saying internally consistent, or do they contradict themselves or use logical fallacies? What other people tend to believe this story? (Did your college professor who has a PhD and presumably a lot of experience in finding the truth recommend this article, or did your uncle Joe who dropped out of high school?) All of these are questions you can ask yourself to determine if a source is reliable or not. That sounds like a lot, but the good news is, once you do this once for a news source, you generally don't have to do it again—once you decide you trust the BBC and NPR, for example, you don't have to run background checks on everything you hear from them, and can just tune in every morning on your commute or something. And if you're looking for something I personally trust, CNN in 10 does a great job of presenting news stories in a credible, reliable, fairly non-biased manner. It's a daily 10 minute long podcast that explains the most important stories of the day in an easily accessible manner, generally without a lot of rhetoric.
I know, it can be exhausting. And you don't have to run yourself ragged finding out every detail about every single news story. But I would also like to respectfully disagree with what Guesthouse says below about not really needing to care about the news—I believe it is vital that we care, even if it seems like the laws have zero effect on our own lives. For me personally, as a college educated, straight, married white woman, my life is probably going to be pretty okay regardless of what laws are passed. But there are so many people who belong to more vulnerable populations whose lives are turned completely upside down by those same laws. So I can look down from my position of relative privilege and say, "It's fine, my life didn't change, so this law doesn't really matter," or I can use my privilege to stand up for those who can't stand up for themselves (but I can only do that if I know what's going on). To illustrate my point, I'm not personally affected if DACA ends and 800,000 people who were taken to the US by immigrant parents as children lose their path to citizenship and get deported. But those 800,000 people sure are. I'm not personally affected when immigrant children die at the border in US custody, in part because of the immigration policies we have in place, but the families of those dead children certainly are. So if you feel tempted to just give up and not care about the news, that's fine and you're allowed to make your own decisions, but at least be aware of the fact that for a lot of people whose lives are directly affected by the news, that's not an option.
Best of luck with the news.