Here are some things you can do to promote your book on Facebook:
First, make sure you have a Facebook account, and make sure your privacy settings allow people who are not your friends to see your information. (This might mean not putting anything too personal there, but remember you are marketing, so you need to be seen.)
When your book is published, or when you reach any milestone, post a comment and the link to your book on your profile.
If you have a blog about your book, put a link to any new blog post on your profile. This gives you a quality backlink, and if people like your post they will share it with their friends. As long as you make it sound interesting, it won't be spammy.
|Here you can choose to post on behalf of your page|
Here is my Facebook page for Choose to Live!
When you post comments on the page, you can post as yourself, or as the page. If you post as the page, then all your fans will see the book cover instead of your photo on the comment, which is great for promoting the book.
Fan pages can be done with special features to make people sign up to an email list, or get a free download. That is all good, but you don't have to do that stuff if you are not ready for it. The basic version will work.
Add a Find Us On Facebook button or widget to your book's web page. Click on the Developers link at the bottom of any Facebook page to find the Add Facebook to My Website link. The simplest options are near the top of the resulting page. You can see my Like box at the bottom of this page. This allows your readers to Like your page, which then means that their friends can see that they have Liked it, and that gives you more publicity.
Of course, the more active you are with your promotions and networking, the faster your fan base will grow.