I applied online over winter break (by the January deadline), and got an email back about scheduling an interview mid-March. You could either go to NY to interview in person or interview via Skype. By the first week in April we were notified via email we were accepted and had a week to formally accept or decline the internship.
The interview lasted 15-20 minutes and my interviewer was super nice and made it relaxing over Skype, which is inherently awkward. Definitely know the company and throw in some facts when you're talking about it (i.e. I know you have X number of magazines and the first one went to tablet in 2010). Also, study the brands you are interested in and know them really well - maybe throw in your favorite article from the most recent issue in conversation.
Since it was an intern interview, questions were pretty basic, but they definitely ask follow up questions to things you say, so when I talked about being a leader, my interviewer asked what I thought made an effective leader and what my leadership style was like. I answered using examples from my time on the student paper. Also, make sure you know sort of what you want to do- it doesn't have to be clearly defined, they know you are an intern, but know whether you want to be on editorial or advertising.