Be hyper-aware of the product and culture.
Here's the thing about people who say they have a "passion for fashion." What they mean is "I really love the idea of clothes and trends, but otherwise I have no idea what I'm talking about." Behind the glamorous fashion shows and expensive, beautiful clothes, there is an entire industry of faceless people who aren't models, designers, or celebrities—and you will probably work with or for them. Like any boss, you can get a good or bad one, but what matters is that you are totally aware of what's going on in that world. That means doing things as simple as reading the magazine you're interning for.
How do you expect to contribute anything new or different when you have no idea what's already been said, or what people are talking about? Yes, an internship can be mentally and physically taxing—running around town, spending hours looking at spreadsheets and blog posts, but that's also what it's like when you're a full-time employee. It feels like a job because well, it kind of is one. The difference is that you're still paying your dues. But, if you show that you have a serious grasp of current trends, buzzed about brands, and young designers—and fresh ideas on how to cover them, you'll definitely get noticed.