I never understood this, while I'm DEFINITELY not very adept at picking up languages (I pick up math easily, languages, not so much, the wife is the complete opposite), I couldn't imagine picking up a language with a tv and some internet forums....
I say I never got it, because I knew many Germans while I stayed there that claimed the same thing, picked up all their English from music and movies....
Well I had english classes, and I definitely learned a lot there, saying "everything I learned came from there" was an hyperbole. I have the feeling that I learned everything from there: these classes were boring and from secondary 3 on I recall learning next to nothing. You can't learn all colloquialisms while listening to a teacher whose mother tongue is french. I don't recall being taught how to use "(n)either", but I definitely remember the day I understood, thanks to forums.groundspeak.com
It's basically immersion, albeit on a smaller scale. Once you get fluent enough, you can use clues found in the dialogs or texts to understand the meaning of unknown sentences.