In the interview itself, the judge is primarily interested in determining whether you are the sort of person with whom he/she could work. Because chambers can be a close-knit place, the judge often is choosing a companion, not simply an employee. You should assume that anyone you meet in the judge's chambers – not just the law clerks (who often have considerable influence over the selection), but also the judge's secretary – will form an impression of you, and those impressions often are an important part of the interview. Do not treat secretaries and other support personnel as subordinates; give them the respect they deserve as the structural backbone of the chambers.
Some judges may test your substantive knowledge of the law; some may ask their law clerks to do so. But even if the interview is not centered on testing your legal knowledge, the judge (and clerks) will almost always seek to engage you on some legal or other intellectual topic of mutual interest. Do not present yourself passively. Be prepared to talk intelligently and enthusiastically about your courses and why you selected them, about the topics of your seminar papers or journal note, about the substance of your past work or academic experience, about legal topics "in the news," and about your plans for the future.
Ultimately, the overall impression you should seek to convey is that you are grateful to have the opportunity to interview, that you are enthusiastic about the possibility of clerking for the judge and that you would work hard.