How does one prepare for interviews at consulting firms?

Use case study books that are available to practice the case studies in interviews. Often the business schools will have copies of the case study material. In addition, there will be a leadership assessment that is done using examples of projects executed by the interviewee.  Consulting companies like BCG, Bain and McKinsey conduct assessment around Problem solving, structuring, leadership, and empathy/EQ. In addition, some of the questions may require estimations, understanding graphs and doing rough calculations. Interviewee is expected to diagnose the issue, and likely root cause. While evaluating, it is ok to share your thinking and approach to solving the problem. Practicing with your peers helps a lot.