I applied for the internship through my programs career services director. I received a phone call to set up an interview about a month later (GAO was behind schedule due to the budget issues).
I had a 1 hour phone interview with two people from offices outside of DC. The questions focused on GAO's core competencies, such as communication skills, analytic skills, etc. I was usually asked to describe a situation that exemplified those skills. I was also asked to explain how I would conduct a study and how I would prepare a speech. The interviewers were friendly and nice, and often asked followup questions.
About 3-5 days after the interview, I received an email offering me a position.