This is an older (2004) article by Jennifer S. Murray detailing the art of the law library interview, with particular emphasis on the academic law library context.
Murray emphasizes that inasmuch as the panel is interviewing you, you should also be interviewing them. She includes a long list of potential questions to ask, to help you conduct your evaluation of the library.
Although things have very likely changed in the eight years since this article was written, it’s still a strong foundational article, setting out things to think about step-by-step as you make your way through the application process. Murray closes with a line about how to deal with rejection, which I found helpful:
“While not receiving a job offer can be disappointing, remember the experience is valuable and will undoubtedly contribute to your eventual success.”