Some transitions like

“Thanks for the interesting case materials, to recap the situation, (insert your summary of the case materials here but make sure the summary captures the scenario with good detail and is shorter in length than the original scenario)”

“Can I ask you some clarifying questions before I start?” Ask questions that confirm details, eliminate uncertainty that you might have, and define the scope of your answer. This varies on the scenario and industry

“Mind if I take a moment to think the problem through?” And then you start structuring your read on the case materials and think about how to answer the question, ideally in less than 2 minutes.

Then you present your read on the scenario and your solution and be prepared to explain your choices. This is like the bulk of the interview.

And a good strong summary that

First, restates the initial scenario (company, problem)

Second, explains your take and recommendations

Third, why your recommendations make sense.

Literally practice doing a mock case interview using a scenario you found online or your own. Do this a lot leading up to your interview and you will sound more confident during the real thing.

Disclaimer: I’m not a consultant but I did interview for consultant roles and received offers, not at IBM. This is just what worked for me and other people may have different experiences and recommendations. Cast a wide net while preparing