One of the best confidence builders is preparedness. So, you should first ask if the interviewer provides the questions ahead of time so you can have answers prepared. Many interviewers do this to avoid dead air (if radio or TV) and to make for a more engaging interview.
But if they do not offer such a gift, or if you're stopped by a fan and asked something you're unprepared to answer, you may end up making a comment you'll regret for the rest of your life and that can ruin your career (just ask Don Imus, George W. Bush, or Michael Richards).
Below are some common interview questions for writers and authors, and then some tips on how to prepare for an interview or appearance.
1. Talk to me about your legal troubles.
2. Where do you find your inspiration?
3. How much research did you do for this book (even for fiction)?
4. What do you say to the people who have been saying that this could have been written by a 5-year old or that you need to find another line of work?
5. Are you happy now?
6. If you could do it all over again, what would you do differently?
7. Who are your rivals / whose work do you detest?
8. Tell me about your political views.
9. Do you feel there are two different (your name here)?
10. When are you completely satisfied with your work?
11. What things do you not like to do and why?
12. Best advice for other authors?
13. Any current love or heartbreak stories you'd like to share?
14. Your work is very similar to "XYZ". Did you "borrow" ideas from that or any other work?
15. What did you think about Jane Doe's "(enter name of work here)?
16. What was your biggest obstacle when writing this piece?
17. (Recent Hollywood Disaster like Lindsey Lohan) says you'd be the one person she'd love to have drinks with. What do you think about that?
18. Before this, have you had any other successes as a writer or author?
And here are some key points to remember for any appearance or interview:
1. Dress the part / be professional
2. Sit up straight
3. Look the interviewer in the eyes (for practice on keeping eye contact, go to a public place like a mall and just walk around. Play a staring game with everyone you pass (but don't be creepy); this will build confidence more than you'd think!
4. Research the interviewer; read prior interviews they've done
5. Know what you want to talk about
6. Have at least 3 transitionary/segue statements ready to get back on topic after an unrelated question
Hope this helps!