After applying via their website, I received an email several days later from someone in HR, asking for when I would be available for a phone interview. After setting up the interview, they also emailed me information about Epic's technical assessment, which you schedule yourself through an online proctoring service.
Next came the phone interview. This was a fairly casual conversation that lasted about 40 minutes, largely because I had a lot of questions about Epic, and what they technologies they use in their software. The person that interviewing me was a software developer himself, as well as a team lead. He asked basic questions, like 'Why Epic?', 'Why computer science?', and also about a project I had worked on, and how I might improve it.
A couple days after the interview I did the technical examination. This is a long, multi-part online exam that tests your math, logic, and programming skills. The exam was proctored, so someone was watching me through my webcam. The exam lasted over 3 hours for me, and I was definitely underprepared for programming part. If you are a CS major, you will have to solve algorithm problems, and implement the solutions in a real language, e.g. Java. My advice would be to practice by solving as many of these sorts of problems as you can find online, or in books. One of the problems clearly called for a dynamic programming solution, so those would be good to practice.