What do people mean when they say that they trust a news media outlet? That's hard to say. For instance, I listen to NPR all the time. Do I trust NPR? Well, yes, if by that you mean that I think that reporters on NPR are mostly not trying to lie, that their journalists assert more true statements on the whole than false, and so forth.
But do I trust them to tell the truth, the WHOLE TRUTH, and nothing but the truth? Ummm...No. That's because NPR is extremely liberal and has a heavy liberal bias in its reporting.
How can I say that they have a heavy liberal bias if I think that they say more true things than false on their programs? Because of what they do and do not say.
You can tell reporters' and media personalities' political positions by (a) the topics and stories they choose to cover or not cover (e.g., about every other story on NPR has something to do with racism/sexism), (b) the questions the reporters ask and just as importantly do not ask, (c) the true statements that they do and do not express, and (d) the false statements that they let interviewees get away with saying without follow-up.
Is Limbaugh conservative? Of course! He says so! And even if he didn't, one could tell by the topics he covers, the questions he asks, the questions he doesn't ask, and so forth. Should you trust Limbaugh? Well, if you're a liberal, you shouldn't trust him to give the best arguments from the liberal side. Nonetheless, no one should be deceived by Limbaugh since he wears his conservativism proudly on his sleeve, unlike (blind? lying?) NPR personalities who regularly deny or deflect accusations of liberal bias.
Of course, one can't always tell the view of a reporter. It took me a little while (not long, but a little while) to figure out that Charlie Rose leaned left. But Jim Lehrer of PBS's NewsHour is about as objective and non-biased as they come--I have no idea what his political persuasion is. Still, polls show that most journalists are left leaning so if you have to guess, go with the data.