Talked to an employee at a Riot-hosted event at my college, who referred me to a company employee with whom I could talk about my potential involvement in the company. After speaking with him about my work an interests, he recommended I apply during the official internship process later that year.
When the intern applications opened, I submitted my app, which simply included my resume and a free-response cover letter. After a couple months (right in line with the stated response timeline), I received an email stating that I had been selected for the first round of interviews, and asking to schedule a time.
The first interview was a phone interview with a Data Science lead analyst, and ended up being a mix of technical and personal questions. The second interview was conducted via Skype with two Data Science researchers, one of whom was the person I had spoken with on the phone a few months earlier, and was way more technical. Finally, I was flown out to Santa Monica to visit Riot Games headquarters and have my third round of interviews, which were in person.
The day began with a tour of the offices, Q&A about the employees and process, and of course a couple games of League of Legends. I then began my interviews, each of which was with one or more people on the Data Science team, and each of which lasted for about an hour. The first one was more personal, touching on my background and experience, as well as how and why I thought I would be a good fit. The second was way more technical, and included programming challenges (which were fairly typical for a Computer Science interview) and a couple of more specific 'situational' problems - they would describe a data science problem to see how I would approach it, even though there was no strict right or wrong answer. They also discussed my previous work in the area. The final interview seemed to be looking at how I would do in a workplace environment, with questions about interpersonal relations and communication ability, as well as some technical questions towards the end.