Based on a Track Maven study of 1.5 Million posts and 6000 brand pages here are a few quick pointers that can help you create the engagement that you are looking at for your brand.
Messaging Matters

Messages that are creative, funny or create a level of curiosity in the users mind are most liked and commented on or shared. It is not advisable to make it too wordy as long messages are often not read, though posts greater than 80 words garner two times the engagement.

Asking questions as shown in the post below helps brands engage the audience in the right context. Posts with exclamation get 2.7X more engagement.

Facebook Users Love Links and Hashtags

Adding links to your posts creates an engagement for users as they want to find out more about your product. here is an example of a Facebook post with a link. Posts with Hashtags are known to be 60 percent more engaging.

Timing Is Everything

Facebook posts as can be seen from the infographic below that are posted on weekends get the maximum engagement as there is fewer than 18 percent of posts that are published on weekends while posts that are published on Sundays get 25 percent more likes, comments and shares compared to a Wednesday post.

The most popular time to post is on  Thursday during the Lunch-Hour.

Images & Video  Grab Attention
Posts with images get 37 percent more attention so visual messaging is as important as the text.

 
Engage With Your Audience

Here are some interesting tips from Track Maven  to start engaging with your audience.
* Comment on your own post to get the conversation started.
* Comment and reply to others to keep the conversation going.
* Comment again after the Facebook posts starts to lose viral appeal to boost it up again.
Mobile Friendly Posts
Facebook is the most popular Social Network app by downloads according to App Annie Stats.Short, sweet and eye-catching images with mobile friendly formats work better.