So this post is kinda meta. It has to do with Facebook's "like" state of mind and the content you share.
Let me contextualize this by saying that this conversation is similar to the If a tree falls in the forest and no ones around to hear it, does it make a sound?, thought experiment. Check out the link if you're not familiar with it.
Because those are our three options: to like, to comment, to share. And I would say that these have been intentionally and strategically placed in order of engagement, from a minimum level of engagement in terms of effort to a maximum one.
I would say engagement on all three levels, and not necessarily from every person that sees the post, just in general, is the social media pot of gold.
But for the purpose of this post and first steps, I'm going to focus on the Like button, and the need to always consider making what you post "Like"-able.
Inspirational quotes and cute animal pictures are usually a safe bet. I know, the latter might not necessarily be relevant to your art. The point is, this isn't rocket science, but just something to keep in mind. Because "Like"s are a fundamental currency in the Facebook economy, and one of the few quantitative measurements we have for engagement, with "Share"s being the other one, if you use FB Insights for Pages.
But I digress, these are all effects of making your content "Like"-able, and again, it's just something to keep in mind when you're sharing a comment, a link, or media.
One thing to keep in mind is that the majority of people do not actively "Like" things on Facebook. In fact an article from March on ZDNet quotes the median virality for posts from FB pages to be 1.92%. Virality of posts 20%+ was only 1%.
And don't equate the lack of a "Like" to not liking. If you're wondering how to post content that people like, I would say the best person to ask first would be yourself, followed by your friends, and fellow artists & staff members.
There is no science, and audiences will differ from page to page.
My final point to make would be that making a post "Like"-able is especially crucial when sharing something that might not be the best of news, like the passing of someone in your organization's community to use an extreme example. The content added, that little bit you have the opportunity to share makes lemonade out of lemons, and should be something sweet, something hopeful, something inspiring.
Another way to look at it, is to ask yourself if "Like"ing what you're about to share in it's totality will be confusing or not, to yourself or to others.
No, you don't have to do this with every post, or even with any. But if Facebook is a tool, then I would argue you're doing yourself a disservice not to make the most out of the different ways people have to engage with your content.
It also doesn't take that much more time to ask yourself, "Is this 'Like'-able?".
To that extent, if you want specific examples to give you an idea of engaging content (most of which you're probably familiar with), I'd recommend checking out 6 Posts That Build Engagement n Facebook at Mashable.
On a related note, a good practice would be to look around Facebook as your page (and if you don't know how to do this and don't like other FB pages, well, just keep an eye out for a post about that), and find content they share which you (and theoretically your organization) would like, and do just that.
Because with Social Media, you tend to get what you give,