Next to actually doing things, reading is the best way to learn about anything new. I probably spend a few hours every day reading about what's going on in the fashion, tech, and business world. It's awesome knowledge to have and people will notice. Here's where I get most of the things I read from:
Fashion REDEF is the best fashion newsletter out there. It comes every morning filled with the best reads of the day. I swear by it.
Business of Fashion has a solid newsletter as well.
Twitter is great for following a bunch of different sources and people. Here's a list of all the fashion-related things I follow https://twitter.com/rsiegel/lists/fashion
Instagram is also crucial for staying up to date on recent collections and happenings.
AVC is probably the best business/startup blog out there and kind of a model for this
And then watch "Dior and I" if you haven't already. If you have, watch it again.