I saw the initial job posting on an e-mail that was forwarded to me, applied, then went through an initial phone screen (fit only) with a current Consultant. A couple of weeks later I received an invite to first round case interviews: 2 45-minute interviews, each consisting of a case and fit portion.
My interview advice would be:
1) Prepare very extensively: I'd recommend the materials on caseinterview.com as a starting point
2) "Cracking" the case is secondary: it's the process, and the comfort and smoothness with which you approach the cases that counts.
3) Have a least a couple of strong stories in response to the standard fit interview questions: got tripped up when my prepared story to a leadership question didn't seem to impress the interviewer, and he rephrased his question. On the fly, I ended up giving a nice story, but in hindsight, it didn't have much to do with leadership.