I run the FB page for a non-profit that I volunteer for. So the tips are going to come from that one, since I’ve had a lot more success for it than I have for my blog’s page.
First thing, you need to post consistently. Like every 1-2 days. But don’t overdo it mostly because of burnout for you. Don’t make it all your own content either. Share other pages. Share some funny stuff. Share some controversial stuff. Get people laughing or talking about what you post - that’ll lead to engagements. Know that the thumbs up like is worth less than the other reactions (like haha). Once people get in a habit of liking and commenting, it will literally snowball from there.
One trick I’ve learned is also to like the page posts with your personal account. Even comment on them. They will show up in your friends’ feeds for something you’ve done. It is a little stealth marketing for your account. Also, some people hate being the first to react or comment because no one likes to go alone. Social signals and all that psychology stuff. It really works though to encourage engagement.
Also, once you have about four likes on the post, you’ll see that it will change from John Smith and Jane Doe like this to John Smith and 3 others like this. Click on that 3 others to see the list. Make sure that each person has liked your FB page. If not, use the invite feature right there to invite them to like the page. It’ll put your name on the invite, beware if you are running an anonymous blog. Usually people will end up liking the page because they have already interacted with it. They have some interest. Easy little trick that costs you nothing. On my non-profit FB page, I usually get a 60-75% success rate on the invites.
Contests and giveaways are good ways to get engagement. Caption this photos too. On your posts, make sure to ask a question. End with something like “and discuss” to encourage people to respond. People actually follow those commands, surprisingly enough.