One caveat about tactics is that they must be applied carefully as a natural part of the interview, or else one can miss the forest for the trees, as the saying goes. An effective combination of the "big picture" approach and tactics can be quite powerful.
Before we offer any tactics, let us recognize that we are talking about a dialog between two individuals, which is cordial yet incisive. There are multiple paths along which one can proceed, with no particular path being more right. It depends on your rationale and assumptions, and the interviewer's discretion to pick a particular part of the discussion to probe further. The interviewer is not looking find a perfect answer, but is instead trying to gain insights into your intelligence, thinking, and creativity for problem solving.
The typical setup is to imagine that you (the consultant) are dealing with a client (the interviewer), where the client begins with presenting his or her best understanding of the issue(s) briefly. It is cryptic and requires further probing to gain a handle on the situation. So here we go, in terms of tactics. By the way, these tactics do apply in the real life of consultants, particularly when dealing with clients. But we must warn you that most of them would come across as common sense items for day-to-day use, having nothing particularly to do with Case Interviews.
Act calm: Remember, you are the consultant in this setup: you are trying to engage and help a client. Act with confidence, not arrogance. Do not be nervous, but more importantly, do not act nervous. You job is to convince the client that, even though you may not have the answers to the issue(s) on hand, you are certainly the right person who has the ability, knowledge, skills, and intelligence to find the right answer. Your personality is equally important, if not more. Even when you think you "know it all," you must not come across as a know-it-all, arrogant snob. Be firm, but friendly. Be confident, but charming.
Listen carefully: Listening and hearing are two very different activities. As in real life, some things are said but what remains unsaid may be more important. One consulting firm uses the practice, which it refers to as "what's behind that?" - that is, listen between the lines, because there may be valuable hints. Follow up to find out why the client said what he or she did.
Ask questions, don't interrogate: Feel free to ask questions. In fact you are expected to ask questions. But be careful when asking questions. They should not appear be an interrogation, but as a process that is focused on constructive search for solutions. The questions must be revealing of your thinking in such a way that the discussion makes progress, and instills confidence in the client.
Take notes, not dictation: Writing everything down will take you away from the spirit of a dialog, in which you are expected to impress the client. On the other hand, not writing key information down may challenge your memory later in the discussion. What information you write down and when you write it down also communicates what you believe to be the key bits of information for issue(s) at hand. And you are being evaluated!
State key assumptions explicitly: Two individuals, operating from different sets of assumptions, may reach wildly different conclusions. For example, about 3% GDP growth may lead to significantly different forecasts if about 3% meant 2.75% or 3.25% (a commonly used tactic in politics). There is no need to restate what the client has already stated. However, do not automatically accept the stated assumptions as being correct, unless you feel they are. Consider the following scenario: a city is trying to justify the building of a convention center and an adjoining hotel by doing a financial analysis of the property. Well, the assumptions of the financial model might require redefinition. For example, the revenue model should contain additional tax revenues from the goods and services consumed by those attending conventions. In fact the actual financial model of costs and revenues is much more complex, but you get the idea. It is not important as to what the precise financial model is, but what is important is that you recognize the possible shortcomings of the model and offer constructive suggestions.
Paraphrase to validate your understanding: When you are not sure if you understand correctly what was said, paraphrase in your own words to validate the correctness of your own understanding. This goes for the problem statement, assumptions, and whatever else that you believe is important.
Challenge, but professionally: The client is not always right. The client is often right about most things. It is the few things, which may make the difference between the success and failure of a business. Enlighten the client in a friendly and confident manner. Never say, "You are wrong!" and then go on to offer the right answer. Instead try using techniques like, "Have you considered ______ (fill in what you believe to be a better choice, or an insight worth considering)?" The clients are generally very smart and bright people, and this interviewer is bound to be. What they need is someone who would help them reach the next level of excellence and understanding, not someone who would sit in judgment of their mental faculties.
Stay focused: Avoid redundant talk or meaningless detours into your past experiences. This does not mean that you have to be boring and you can not have a sense of humor or that you can never mention your experiences. You can, but use judgment. In fact, you can apply (and not talk about) earlier experiences, when relevant, to offer insights into your problem solving skills, as opposed to coming across as someone applying something that they had already known. Yes, you would then be a bit cagey for a little unfair advantage, but it is the real world!
Avoid academic formulas: Your ability to memorize, and blurt out complicated formulas, is not particularly valuable. What is valuable is your understanding of what they mean, and how and when they can be applied. For example, the knowledge that a particular form of optimization problem for networks and distribution, which you are able to recognize, leads to a solution with concentric circles is much more valuable than your ability to recite the formula or your claim that you can easily do (non-)linear programming to find the real answer.
Do not look at your watch: Do not do what President Bush did in a presidential debate. You remember what happened to him, don't you? The interviewer's time is at least as important as your time. The interviewer likely has other candidates to interview as well. Let the interviewer be the timekeeper, so you can focus on your performance and acting interested - that is, if you are interested in the job.
Follow the interviewer's lead: Throughout the discussion, the interviewer would give you additional information and ask you to focus on particular aspects of the discussion. Do it, even though you might feel that some other aspects are more important.
Keep the endgame in mind: Remember, you are being evaluated on your problem solving skills, and not on the final answer. The interviewer is picking and choosing areas to probe further, as you move along.
As you can see, there is nothing spectacular about these tactics. They are common sense and part of everyday life. One can make this list needlessly longer. All these are learnable skills, and thus practicing them would help. They should be incorporated into almost all your discussions. If one simply tries to remember them for application in a Case Interview, one is more likely to forget the endgame, and miss the forest for trees. Application of these tactics should be natural, as opposed to rule-based.
Sometimes in interviews, the interviewer is keen on testing you on trivia. Here is an example: Why are manhole covers round and not rectangular? Well, the answer is that a round manhole cover will never fall into the manhole. If this were all that the interviewer is interested in, then we would not consider a set of questions like this as a case interview. However, the interviewer may have a deeper motive of understanding how you might answer a tricky question, or how you would go about solving some seemingly meaningless riddles. Your approach to solving these riddles may offer insights into your thinking.
Assume for a moment that no one knew the answer to the manhole problem. We can generate many hypotheses, which can then be tested for their validity. Hypotheses can range from the use of round covers as being: i) not optimal, despite a widespread use, to ii) posing less harm to humans who must deal with them, to iii) better for easier movement (that's why wheels are round too), to whatever. Chances are that the answer -- round covers would not fall into the manhole -- would be something that we could not come up with as a hypothesis. The reason is simple. Determining -- why some thing is the way it is - is a very complex problem. And the interviewer is just being a smartass if he or she is looking for the right answer. But it is an unlucky break for you. Such is life! Chalk one up for the experience.
Consider a slightly different manhole problem. What shape the manhole covers should be so that they would: i) be easy to move, ii) minimize injury to those who deal with them, and iii) not fall into the manhole, and so on? This is a much easier problem to solve. Hypothesize various shapes, test them against the selection criteria as stated above, and bingo - we conclude that they should be round.
Some of these riddles take on lives of their own on school campuses. Why manhole covers are round is one such riddle. No serious case interviewer would ask you such a question, unless the interviewer is in a desperate need to show you his or her superiority. Our suggestion is get such frightening scenarios out of your mind. Assume that you would be challenged by a serious problem, albeit abstract at times.
Abstract problems are a bit more challenging. Consider the following problem. Who has a better healthcare plan - Gore or Bush? It is a perfectly legitimate question for a case interview, not to determine your political inclination or your knowledge of their plans, but to evaluate your ability to solve a real problem. You are given two alternatives and you are asked to determine which is better - an everyday occurrence in the business environments. But it is a tricky question, if you haven't already caught on. Neither Gore nor Bush knows which plan is better. Both have their own definition (criteria) of what is better and each is hoping that his plan according to his definition is the one that would resonate with the voters. Things are slightly less democratic and more systematic in the business world. To address the original question, you must define the problem more precisely - that is, define what "better" means. It is not Clintonesque or hair-splitting, it is at the core of the problem. Once you address that, it is smooth sailing and you have aced the case interview.
There can be even more abstract problems in case interviews. Some would test your general knowledge along with your ability to solve a problem. Consider the following problem: How many lemons should you order to serve lemonade for a gathering of 1,000 people? Wow, sounds like a lot of work! We are not lemonade experts, but through a series of assumptions and questions, one can come up with a reasonable formulation pretty quickly. Depending on the size of the lemon, we can make one glass of lemonade per lemon. About half the people would be interested in lemonade (the rest would be busy drinking only the spiked stuff). The party will last for 3 hours. Of the 50% interested in lemonade would drink, on average 2 glasses, and so on. The actual calculations are not necessary, nor is the precision. A directionally correct set of assumptions, leading to a rigorous formulation of the problem, is what is necessary. It demonstrates your resourcefulness and thinking in that, given some time, you can get the information you actually need. Having formulated the problem correctly, you can easily apply the information, to get to the answer.