The interview process was pretty simple. I had only one interview: in person. (No phone interview.) They ask about your favorite TV shows and movies, what you know about screenplays/teleplays, and how your workload at school will fit into this internship.
I interviewed for a development intern position at Pretty Matches Productions, which is Sarah Jessica Parker's production company within HBO. It's definitely good to be familiar with SJP's work, but probably best not to come off like a fanboy/fangirl during the interview.