This is a difficult question. There is some justification for being hesitant to trust mainstream news on foreign policy, because they were behind the push for war with Iraq. They have since apologized, but I have fears with Iran becoming a threat, we may hear the same rhetoric again. However, with domestic issues, they are more reliable.
To go outside of the mainstream, you should still keep your critical thinking hat on. What kind of source is it? Does it produce reliable information? Is it funded by a special interest that could affect objectivity? Who are the main contributors? Fox News has shown themselves to be completely inept when it comes to informing people. Multiple studies have shown they do a pathetic job of informing people, so it is highly pertinent to evaluate alternative sources correctly.
You could also try looking for websites run by academics. With science related information, you can look to the scientists themselves, and see the fact that the majority of climatologists believe the earth is warming mostly due to human activity. Or with Supreme Court opinions, those are available for free online; and every politician now has a website, so if you think the media is "lying" about them, you can go read their opinions directly. Or you could look at foreign news sources, and see how they interpret events happening in the United States.