The entire process was very quick and I applied online through a job search site. After a few weeks, I received a call for a brief phone interview. We scheduled an in-person interview for the upcoming Friday. After the interview they told me they'd give me their answer by Wednesday (they even got back early on Tuesday), and I began the position the following Monday.
The interview itself went great. It lasted about an hour, and was a very good balance of being told more about the company and what they were looking for, and me talking about my experience in the field and the skills I could bring to the table. Besides being helpful, it was a very fun and engaging interview to sit through.
I accepted, and the internship has been wonderful.