All you have to do is to post a status inviting your audience to ask questions about your book or writing, and then use the Reply feature on Facebook Pages to answer each individual question. As you may know, only a fraction of the people who’ve liked your author Page see your posts at any given time , so you’ll need to do some pre-promotion to make the most out of your Live Facebook Q&A.

http://blog.bookcountry.com/host-successful-live-facebook-qa/