Star Trek often overlooks all this, often times implying the ships' databases contain all information known rather than accessing Space Google or Wikipedia or Memory Alpha. Hell, it even got to the point where Janeway could look up the Excelsior's maintenance logs.
How they get their news is an interesting question. Since there is no television, one would think that must mean newspapers, or perhaps a digital version of them. Certainly, Jake Sisko seems to be a newspaper journalist. But then, all the reporters we see in Generations seemed to be filming everything, so there must be some sort of visual medium for news broadcasting.
Since no one foresaw the rise of Facebook or Twitter even in the 1990s (I think Facebook was only just starting off as a university only thing when Enterprise ended) we don't see that aspect of Federation life. Strangely enough, the Abrams movies don't even feature social media of any type. Perhaps this was eradicated in WWIII?