I guess it’s the most frequently asked question when it comes to languages and, unfortunately, it’s impossible to give one answer. The word fast is rather relative since the speed in making progress can enormously differ as it depends on the type of person that we are working with.
To generalize as much as possible, from my personal observations I think that watching films and short videos only with English subtitles is a great way to learn quickly and effectively. Let’s not get too excited, though… It is definitely not enough! Learning new vocabulary systematically, preferably via useful apps such as Quizlet, is also vital, especially when you get new words from those videos! Imagine watching a short programme or an episode of your favourite TV series where you are actually interested in the words that you hear. I can promise you that it will improve the speed of your learning process significantly (not to mention the sheer watching pleasure)!
In my opinion, the worst thing you can do is to excessively practise rules of grammar until you completely drown in handouts and copies. It’s an obsolete method taken from public schools where they need to comply with certain rules and time limits. Limits? Huh? For you, there are none. Remember that!