I submitted my cover letter, resume, and transcript online through my school's career website. I received an email notifying me I had been selected for a phone interview. I had two one-on-one interviews with current analysts over the phone. Each interview lasted about a half hour. Half of each interview was a case-interview, usually a simplified version of a case Cornerstone worked on. The interviewer presented the problem, asked how I would approach it, and then guided me through some calculations. The other half of each interview was "behavioral," but it felt much more conversational than some of the "tell me about a time you did this and that" interviews I experienced elsewhere.
Within a month I was invited to DC for a final-round interview. I got there a bit early, but one of the analysts gave me a tour of the office and introduced me to everyone. All the employees seemed very friendly and helpful. I had five 1:1 interviews. Three were with analysts, one with a manager, and one with a senior executive. All had the same format as the phone interviews except the last, which was a more informal discussion and had no case questions.
Between interviews I went to lunch with a couple of analysts. Beyond the great food, I got to ask lots of questions about working there.
For the behavioral portion, be ready to talk about leadership and teamwork experience. Know why you want to work for Cornerstone. Know what to say.
For the case portion, just relax and try to think creatively. Explain your reasoning at every step. It won't ruin you interview if you make a few arithmetic errors, or even if you make a minor logical error. There's no specific background information you need.