The short answer? Practice, long-term paying attention to the news and seeing if what the source in question says has been true before, and awareness of events in general so I can tell if something sticks out like a fake, sore thumb.
The long answer? There are a few ways, I guess. The most obvious is to pay attention to several news outlets, all across the political spectrum and even from other countries (like the BBC). This helps discern what really happened in the same way that having two eyes helps determine depth and how far away something is, because you get it from several angles. If they all have some news in common, and you can account for known slant, it’s probably true.
Another way is to do the research. Sometimes the Left or the Right get all riled up about a bill that’s being debated in Congress, over-reacting and telling you that we’ll lose our access to herbal medicine, say, or that we’ll have “death panels.” However, if you go to the bill itself and read the actual text (the definitive site is thomas.loc.gov) you can see for yourself if they are posturing, or how much they’re mucking up the truth.
Also, it helps to know what sites are authoritative sources to find information. Joe Blow’s Blog probably isn’t the best place to find out anything but Joe Blow’s opinion (although you can also fact-check Joe Blow and see if he’s generally a good source of opinion), but if I wanted actual information on the national debt, say, I’d go to Treasurydirect.gov. If I want to know unemployment or inflation statistics, I go to bls.gov, which is the site of the Bureau of Labor Statistics. NBER.org posts the official start and end dates of the recessions in the US. A good source for abortion info, if you want to get involved in that brawl with someone someday, is the Alan Guttmacher Institute – They seem to be the only group in the entire fray that is trying to compile reliable statistics. Primary sources are great. Have a question about the Constitution? Read the Constitution! :)
Finally, sometimes you might not know the slant or opinion of a purported news site. Sometimes you have to watch their stories for a while and compare them to other sites (especially definitive ones) to know what’s going on with them. For instance, if you’re like my Mother in Law and all you watch is basically Glenn Beck, you might begin to think that he’s a definitive source for news – but if you take what he says and evaluate it based on observed reality (taking a statement like “There’s no such thing as climate change, because the climate isn’t changing” and comparing it to statistics, news about the Solomon Islands and Florida losing ground to rising water, and how the diseases that one might expect to spread when the climate changes are spreading in the predictable way), you might realize that the news source you’re evaluating is or is not reliable. This just takes time and observation.
Another way of determining slant might be to look at who owns the news outlet in question. Who profits from their reporting? Who pays them their wages? Can you discern an agenda? That sort of thing.
Sussing out reliable news takes work – sometimes, I think most people are unwilling to put in the work and just believe everything they hear, or everything their political party tells them. However, I think the work is worth it, when trying to be a good citizen. :)