Because Facebook is the most popular social network right now, you want to have an author Facebook page. This is different from your personal profile. A page will allow you to see insights on which posts are most popular and when your fans are most likely using Facebook. This helps you create posts that your audience will want to share and you can post them at the times most likely to be seen by your fans.
Everyone seems to be on Facebook and enjoys sharing updates and fun images. Since Facebook is a social media network, it shouldn't be used just as a promotional tool. Use it to engage with your fans by asking for their feedback, sharing valuable tips from your book, answering reader's questions. You can even post short videos and do live videos to connect directly with fans.
To see how well your posts are doing, click on the "Insights" tab to find data related to the number of people who have seen your posts over a specific period of time. The numbers represent your fans and friends of fans who have seen your posts. You'll want to check your page views in Insights as well to see the demographic of your audience.
I recommend your Facebook page be about you as the author, not a particular book. You may have more than one book and don't need to set up a different page for each book. Your Author Facebook page can be used to let your fans know about your newest book. It's not enough to have just a Facebook page though. You want it in addition to your website to get the most exposure for your book(s).
So now go and create a Facebook page here. Once you do, share the link below in the comments. And as always, let me know if you have any questions.