The first part is getting the interview set up. From the hundreds of applicants they will select typically 10-15 intern candidates to interview in person. Someone will call you to set up the interview, usually a week or so out.
The interview was pretty straight forward. You bring your portfolio and resume and present your work. Usually you will present to 3-5 people (I presented to 4). Michael Prince will usually come in last, flip through your portfolio and ask you some tough questions or call you out on flaws. Such as, why did you go with this material rather than that? Where do you show your design inpiration? Why is this inconsistent...etc.
The interview day takes about 4-5 hours. After that they will contact you if you got the job or not in about a week or so.