I interviewed (and was hired) for in-house clerkships with corporations. Typically, the interview is a little different, because they use the more common "behavioral" interview that corporate America is falling in love with. I've also had a few behavioral questions when interviewing with government agencies. Just in case you didn't know, there is a widely-suggested format for answering the questions. You shouldn't sound like your answers are memorized, but in your response, the interviewer is looking for specific examples and explanations of your behavior in the past. I usually think of about 5 or 6 "canned" scenarios or problems in my past jobs that I can draw from when answering these questions, but my response is not memorized and I make sure that it is responsive to the question.
The behavioral question will ask, "Tell me about a time that you did xyz" or "Describe an instance where you had to (use some quality, like persuasion, problem solving, conflict resolution with peers, etc)." The interviewer is looking for specific examples of something you've done, on the theory that what and how you've done something is a better predictor of your aptitude for the job than just saying what you think about something.
So, the answer should be specific. In your answer, remember "S.T.A.R."
Explain the SITUATION (background, context, a little something to explain why you had to act.
Explain what your TASK was.
Explain your ACTIONS in resolving the situation (This is probably the most important)
What was the RESULT. What did you learn, how did it help, anything quantifiable, was there follow-up, etc.
Good interviewers will prompt you once or twice if you veer off course. Take that as a cue that you're missing something and get back on track.