After finding the company on the Inc 5000 list, I submitted my resume/ cover letter to the emails found on the company home page. I sent it to three different offices (NYC, Philly, ATL), and received three responses.
I had an informal phone interview, followed by an in-office interview. My interviewer was very nice, and the process was conducted much more like a conversation than an interrogation that most interviewees experience at one time or another.
I heard that I got the internship within 2 days.