The thing is, vocabulary is so diverse, and gets really specific depending on the genre of whatever media you're consuming. I'm an exchange student at a university in Japan, and by that I don't mean I'm doing a study abroad program, I mean I'm taking the normal curriculum for my major, same as other students at the university are taking. The Japanese that's used in the classroom is fine, I can talk about a whole range of topics, and generally encounter very few language issues living life here. However, whenever I've gone to watch some fantasy show with some chuunibyou-ass vocabulary, it can be hard to follow. And all the the different genres have their own specific lingo that I don't really care to learn in order to watch a couple shows I may be interested in seeing, so I just don't. End result is I watch a lot more shows set in "real life".
To answer your question:
It took me 5 years of semi-dedicated study, in high school and then university, to get here, and I can watch some shows. I have no idea how long it would take for me to have such an expansive vocabulary as to be able to understand all of what's being said in any anime.
As for studying, while I of course self study on the side, I can't really advise you on how to self study in lieu of a classroom setting, since the bulk of my language education comes from university, and life experience in Japan.