I belong to a few author-centric Facebook groups, and this is a question I see pop up from time to time, so I thought I'd weigh in with my thoughts on the matter.
I don't claim to be an expert, but my Facebook page is my most important tool for keeping my fans engaged, and for roping in new ones. Here are some observations and tips that you may be able to apply to your own pages.
What sort of content should I post?
Whatever the hell you want. Try some different things and see what works for you. The most important thing to remember is that whatever you post should provide some kind of value for those who see it in their feed.
Before you post something, consider it from the point of view of someone who likes your page.
The classic example of a terrible Facebook post is "Check out my books!" followed by a link to said books. That works about as well as approaching strangers in a bar and begging for sex.
Sure, the whole point of everything you post is to sell more books, and there's something to be said for honesty, but that sort of post just reeks of desperation.
The people who already like your page know you have books available. You're providing no value for them. And they're about as likely to share your shitty post as the woman pictured above is likely to call all of her single friends and ask them if they want to boink this creep at the bar.
So what should you post? You're only as limited as your imagination, but here are a few things to think about...
1. Post funny shit.
Unless your books are exclusively about AIDS or the Holocaust, in which case chuckles are probably not in line with the tone you want to set, an easily digestible laugh will almost always be appreciated by people scrolling through their Facebook feed instead of working.
I have an advantage here because I write comedy books, and if I can make people laugh in a Facebook post, who knows how much more I might be able to make them laugh with something I took a lot more time and effort with?
2. Include images.
A good and/or relevant image can make all the difference as to whether or not a person casually scrolling through their Facebook feed will stop long enough to bother with a post at all.
3. Funny Shit + Image = Meme
There's a reason memes are so popular. It combines the scroll-stopping power of an image with the easily and nigh-instantaneously digestibility of funny shit. Photoshop a bit of text onto an image and post set it loose. If it's somehow related to the content/themes/whatever of your books, all the better. For instance...
This is more complicated than a meme needs to be, but it's a good example of what I'm talking about. I start out with immediately identifiable Star Wars images to catch the eyes of nerds, because I write fantasy books. The ones who will get the joke are he ones most likely to be familiar with Dungeons & Dragons' ridiculously complex grappling rules, and subsequently more likely to be the sort of person who will enjoy my books. And then at the end there I filter out the interest of anyone who is going to be offended by the word "fuck", because those people are almost certainly not going to enjoy my books.
Speaking of which...
4. Don't try to please everyone.
It's just not going to happen, and you may end up shooting yourself in the foot by pulling your punches to avoid offending people. A good example of this is all the shitty writing-related memes you see on some author pages. It's safe, sure, but who gives a shit?
A lot of people will tell you to avoid posting about politics. I'm not one of those people. If Donald Trump has given us anything in these dark days, it's a wealth of material to work with. And if there was ever a time when you could make fun of a political figure without worrying about offending people who are likely to read books, this is it.
I know you want to see the number of likes on your page grow. We all do. But it's more important to do your best to make sure the people who are liking your page are people who are also likely to enjoy your work.
For example, if you write paranormal romance, you probably don't want me to like your Facebook page, because I don't read in that genre. Facebook only shows a fraction of your audience a particular post. I believe that percentage grows if a post has more interaction (in the form of likes, comments, share, link clicks, etc...), but if I'm one of the selected 10% (or whatever. I don't know what the actual stats are.) who sees your post, I'm going to just keep on scrolling, and your effort will have been wasted.
Consider this image...
I posted that last night. It has 89 positive reactions, 18 shares, and a reach of 3,099, roughly 75% of the number of likes on my page, and I didn't spend a dime boosting it. Did I lose a couple of likes because of it? Probably. But I'd be willing to bet the ones I lost were dead weight anyway. And some of those people who reacted positively are people who don't already like my page. More on that further down.
The bottom line is that people who find that picture funny are people who are going to enjoy my books, and that people who don't are people who can fuck right off.
Am I saying you should post a bunch of political shit and/or actively try to piss people off? Of course not. But don't let fear of breaking a few eggs keep you from making an omelet.
5. Share snippets of your work(s) in progress.
The people who like your page are (hopefully) fans of your work, and are eagerly awaiting your next release. But writing a book can take a long time. You can keep them from forgetting you exist and reassure them that you're actually working on something by sharing a sample of what you're working on.
Throw the fans a bone every now and again, but don't throw so many bones that they'll be able to form a skeleton. By that, I mean you don't want to give away the whole plot of the book, or all the best parts.
Again, I'm coming at this from a comedy point of view, but it probably applies to other genres as well. Here are my rules of thumb for sharing samples of my writing:
Funny out of context.
A small fraction of what I've written that day.
6. Post new releases and promotions.
Yeah, you don't want to be posting "Buy my shit!" all the time, but when you've got a new release, your fans want to know. That's a big part of the reason a lot of them decided to like your page in the first place. And if you're running a sale, they'll appreciate being able to pick up books in your backlist that they haven't yet gotten around to reading at a discounted price.
And if they've already read all your shit, they aren't going to begrudge you a bit of self-promo every once in a while.
7. Share other people's shit.
Some Facebook pages do very well for themselves posting almost nothing but a bunch of shit they found on other pages. And if you share someone else's post, they just might be inclined to share yours in return.
I don't mean to suggest you get into a circle jerk of reciprocal post sharing. Your followers come before all else. Share things that they will find interesting. Maybe it's a blog post, or a funny meme, or a promotion or new release by another author whose books you think your own fans would enjoy. That may seem counterintuitive, especially if that author is more successful than you are.
But think about what you've done. You've provided value for your fans. You've done a favor for someone else who may or may not remember sometime down the line. And if you get enough of your fans to buy this other author's books, there's a chance that Amazon will pick up on it and include you in that author's "also boughts".
How do I get people to like my page?
Nothing's sadder than a brand new page with zero content and zero likes. The content is up to you, but those precious likes can be hard to come by. I've found that success begets success, so it's probably a good idea to hit the ground running with some seed likes.
You can invite as many people as you want from your personal Facebook profile to come like your new page. Once you get yourself established a bit, I recommend discontinuing that in favor of keeping your business life and private life separate, but in the beginning you'll probably find there's enough crossover such that you don't have to post content to an empty theater.
Your Facebook friends are a limited source anyway. So how do you grow beyond it? There are a number of ways.
1. Make sure you have a link available wherever appropriate. I always put one in the back matter of my books, and at the end of each blog post. Hell, if I happen to mention my Facebook page in the meat of a blog post, I'll hyperlink that there as well.
2. Pay to boost your page. I've never done that, so I don't know much about it. I'll pay to boost specific posts that I think might do well with a bit of a push, but I don't know. Paying to boost my page just feels kind of sad and futile. No offense to any of you that have done it. It might well be a great thing to do, and I might one day find out. But I haven't yet, so that's all I've got to say about that.
3. The most important thing, in my opinion, that you can do is to keep posting quality content that your friends will like and share, roping in some new likes to your page from their friends. That can happen organically, but there's also a way to give it a bit of a nudge.
Remember that Trump post from before? Take a look at the reactions to that, indicated below by the crappily drawn red arrow.
When you click on the people who reacted to one of your posts, a window should appear on your screen (This only works on your computer, by the way. As far as I know, it won't work on your phone.) showing you the list of people who reacted. On the right side of their names, there will be buttons which tell you that someone has already liked your page or has already been invited to do so, or which allow you to invite them, as indicated below by the crappily drawn red arrows.
No one I've asked knew about this feature before I showed it to them. I figured it out by accident a few months back. But it's just one more reason to keep putting out quality content.