Epic does fantastic work at getting the right people in the door and through the process. They also make a point of letting you know your status (accepted, rejected, etc), which, for rejections, is unusual for most employers. This makes a huge difference, and is one indicator of why they're such a great company. If you're coming form college, look for career fairs or job-board postings, and contact any alums that work there. If you're post-graduation, go to their website and apply online. If your GPA is greater than a 3.5 and you've done impressive work related to the applied-for role, then you're likely to get a phone screen. the Phone screen makes sure both parties understand what the job entails, and that there's nothing obvious that disqualifies a candidate. If that goes well, you'll take some tests. These are super-important, as Epic uses metrics to systematically (and thus unbiasedly) critique your application. If you aren't used to logic-based tests, brush up on those skills...but other than that, there's no way to study for them. If you get an in-person interview, dress comfortably (no suits required) and presentably, and be yourself. If you're trying to play a role, you'll come off awkward -- be your awesome self, and hopefully it'll be a good fit.
Epic usually responds to all candidates, through all stages, within 1-2wks of the last milestone.