You already know the answer: about the same way you interview a lesser (known) mortal, except as humble as that person is (it happens!) they still expect a bit of deference…
The real question is, how do you get to interview a famous person?
Let’s assume you are doing this as the core of an article, or your talk with them is one of several interviews for an article. And you are proposing the article (with the interview) to the editor.
First, figure out what that interview is about, then list the best known people with something worthwhile to say. Send a lively, well crafted query letter to the editor, sell your idea, and suggest who you would like to interview for that piece. You can try many editors of different publications, but one at a time, best first.
Only when you have one clear “go-ahead” (a “let me see it”) do you approach the famous person for a short (think 15-minute maximum) interview, telling the name of the publication that gave you the go-ahead, what the article is about, and asking if/when the interview can/will be held. The conversation will probably be by phone, e-mail, or in person, and you can ask for the interview the same way (if the person has an agent, that’s the best approach; by e-mail is the least advisable means).
Then all that remains is the actual doing, and since you are both on the same track and know the purpose of the verbal exchange, the rest is straightforward. Thank them first, start with a fairly broad but pertinent question. Make the most important question the second one, and if you can segue into it from what they’ve just said, all the better. (The less obvious the questions, the fresher the answers—usually!) If you have a talk-stopper to ask (“Did you really kill the butler?”), ask that last.
Don’t talk about yourself (unless they ask, then quickly), keep the conversation friendly but professional, laugh if they say something funny (or meant to be funny), and consider ending the interview with “Is there anything I didn’t ask that you would like me to include?” At the end, thank them again, and assure them that the moment the article is in print, you will send them a copy. (Get an address if you don’t already have it.)
Remember, they are speaking with you because they somehow benefit from being in print. But their time is valuable and you will get only as much of it as you deserve. So be a journalist first, research the person fully before making contact, and stick to the topic. Only if they wonder off, let them go, take notes, and gently herd them back into the desired corral to get the information you need—unless what they are saying is even more important. Then follow them with notes wherever they go..
Have I actually interviewed famous people? Yep, five Presidents (alas, all of South American countries), movie stars, sports figures, Adlai Stevenson four times, others. My conclusion: they are just like anybody else (but famouser) if you are courteous and acknowledge your gratitude. Sometimes they are even very funny, and they are almost always articulate (if they are sober). Which is why I almost always interview in the morning. (Not for me—I don’t drink. They do!)
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