I've studied Polish mostly from reading and listening to books. The first book I ever read in Polish, was Harry Potter. When I first started to read Harry Potter, I had only been learning Polish for about a year at the University.
While I did enjoy that class (mostly because of the professor) it was basically all grammar, grammar and more grammar. At the end of that year, I couldn't really speak or understand Polish normally.
I started reading the first Harry Potter book in January of 2008. It took me four months to finish it. Honestly, it was extremely difficult and took a lot of commitment. But after finishing that book, I really felt like I spoke Polish. My brain was able to produce and understand Polish automatically!
While the first book took me four months, I managed to read all seven Harry Potter books before the end of that year! Each book was bigger and bigger, but I managed to read each one faster and faster. I read (or rather listened to) the last book in only a couple weeks. My learning accelerated exponentially.
First, I read and simply tried to understand from context. Later, I would go back over what I read and look up all the words I didn't know in the dictionary. I created flashcards on the computer for all these words. Everyday I reviewed my flashcards.