I have been studying English for ten years at school and then attended a university for four years, where curriculum was taught in English. Then I had a job with an American company for 8 years. Nonetheless, when I was opening an American or a British newspaper after all this time of learning and perfecting my English, there still were unfamiliar English words. That was frustrating.
In my opinion, if one can read newspapers without, or with little use of, a dictionary, he or she should be able to read pretty much everything in the foreign language one is studying (perhaps, with the exception of certain works of literature).
That's why, when I began to study German in February 2014, I have concentrated my efforts on reading German newspapers and learning words. Just as I had thought, German newspapers proved to be a treasure trove of new words and expressions. Now, in 2017, after almost 3 years of reading German newspapers, my German word list consists of 25000 words and expressions. Depending on the longevity of my daily German readings, I keep adding to my word list every day from 0 to 20 new words/expressions (you can download some of them here for free).
So, in answer to your question, the best and fastest way to build up your German vocabulary is to read German newspapers. You will not only be able to expand your German vocabulary, but also keep yourself entertained and up to date with the German and world news.