Initially contacted the designer via email, which I were able to get through my college's career website. She replied back within a week and arranged an in-person interview the next week at the company building in NYC.
I went in and the interview process was about half an hour long, I met with two designers at the same time. I showed them my portfolio and talked about my work and interests. They asked me what I knew about the magazine and how long I am able to intern.
They told me that they'll get back to me the following week, which they did.