Instructions
The Author's Website
Go to the author's website. If you don't know it, typing the author's name into any web search engine should produce it fairly easily.
On the author's website, locate and click on the tab labeled "Contact."
Review the contact methods listed as well as any specific instructions. Many will provide an email or mailing address, along with a preference for how they wish to be contacted.
Draft your question respectfully and in as short a format as possible; lengthy and involved questions are less likely to get an answer, as are those that request information the author is not likely to give, such as whether two main characters will form a relationship or not.
Send your question via the author's preferred method, and be prepared to wait a lengthy amount of time for an answer, as the author probably has a large volume of fan mail and only a small amount of time allotted to opening it.
The Author's Official Facebook Page
Many authors do not offer an email or mailing address, instead listing a Facebook page on their website. If so, follow the link given to the author's Facebook page.
Once on the author's Facebook page, click "Like" to have access to their comments wall.
Type your question into the comment box and post it to the wall. Try to keep it short so that you aren't taking up a large portion of the author's wall with your question.
You will receive Facebook notifications for any responses received; other fans will be able to see your question and you may obtain your answer from someone who has already asked the question. This cuts down on the author answering the same questions over and over and also allows the fans to chat.