I ended up talking to a recruiter for the company, knowing nothing about it, at a career fair my school ran. He was very kind, and very enthusiastic about his job. I gave him my resume, and he got excited looking at some key points on my resume that he felt would be a good fit for one of the intern positions at his location. Asked for his contact info, and was referred to company email (only because he had ran out of business cards for the day). I did not hear about anything for 2-3 weeks following the career fair, after having emailed the company site. I looked online and applied to as many intern positions as I qualified for / was interested in. There, I put down the recruiter's name, hoping to grab his attention.
From there, he responded to me within a couple weeks, and I was then scheduled to have an on-site interview. I had no phone interview, which surprised me. I was told later that talking to the reps in person at the career fair counted as an "initial candidate scan."
I was at the company site (Marlborough, MA) for about 2-3 hours, talking to 4 people for 30 minutes each. I ended up talking to employees there for so long that the main recruiter came back to talk to me for even longer about the position. I asked about how quickly they would be able to respond, and they said that they needed to screen the rest of the candidates before making a decision.
From then on, it took about a week to receive an offer, though I know that they were in a rush to extend offers before too late (which was good for my personal anxiety). A week of waiting felt so long! From there onwards, it was very easy. The company was so accommodating, and I felt that I had been given far more than what I expected.