First, you complete the online application on Viacom's website. If a member of the College Relations Team likes your application / resume, you will get an email to set up a time to chat on the phone. This is NOT a phone interview, it is just talking with one of the CR staff to see what your interests are, and then they will refer you to departments that may be of interest to you (e.g., public affairs, marketing). This is the time to make it clear if you want a specific TV channel too (e.g., MTV, Spike).
Then, you will interview with the person you got referred to. They are usually flexible and will do a phone interview if you are out of the general NYC area. If you do not get offered the internship, you can talk to the CR staff member again and get referred to a different internship. This happened to me; I did not get offered my first internship choice, but got offered my second... and I'm so glad I did because I now feel like that this second internship option is a way better fit for my interests!