CFI Interview
A lot depends on the operation. A 141 interview will likely involved a written exam(s), a sim and/or flight, an interview with the Chief Flight Instructor and, perhaps, a board interview with training managers, supervisors, standardization instructors, etc. You should find out beforehand if you will have writtens and flights.
An FBO interview may be with only the boss and/or his Chief Flight Instructor. You might have a flight.
Be prepared to answer questions about your training, flying background and goals. Answer any goals questions candidly. Don't tell them what you think they want to hear and clarify, if necessary. If you're asked what your short-term goals are, answer the question just as you hear football players answer questions about their goals, which is always to win the next game; in your case, to get this job. If your eventual goal is the majors, say so, but be sure to add in something to the effect that while you're there you will devote all your energies to providing the best flight instruction possible, that you will do everything necessary to build the business, and when you leave you would hope to leave your job in better condition than you found it, etc. Give illustrations of past jobs where, indeed, you left the position in better shape than when you found it.
You might be asked about how you would handle certain scenarios, such as a student who is demanding to know when he/she will solo, recalcitrant and "cowboy" students, etc.
Hope these points help. Good luck with your interview. Let us know how it went.