The process took 2 weeks. I interviewed at Paramount (New York, NY) in Apr 2010
Interview
When applying for an internship, MTVN assigns an HR representative to you. Your first interview is with him/her and they are for the most part just trying to get to know you and see what areas of the company you are interested in. They will then set up an interview in the department you are interested in. They also give you the option of selecting a "back up" division in case you don't get your first choice or its not a good fit. I had a series of three phone interviews. They were all behavioral. As long as you sound passionate about the position, you'll be fine.
The process took 1+ week. I interviewed at Paramount in Apr 2008
Interview
initally had a phone interview with a campus recruiter, then went into NYC offices for an interview with a supervisor; very basic questions, super friendly interviewers, felt comfortable the whole time