Your professor will provide you with tools, guides, and practice in the art of interviewing. In addition to many excellent websites about journalistic interviewing, keep in mind that your interview could also be viewed as taking an "oral history" of your interviewee and that term will get you even more tips. The links, video, and books below point out some of these different strategies.
Giving your interviewee the opportunity to expand on your specific questions
What caused this event...? Why did this happen...? What happened next...? Can you describe the scene in one word...? Can you compare two events...? Explain the reason for...? What conclusion can you draw...? What is your point of view about...? Can you describe the scene...? Can you explain a photograph...?
What was the happiest (funniest or saddest) memory? What was your biggest accomplishment? What actions would you change if you had a chance to re-live those years again? What mistakes did people make during this period or event in history?