At the bottom of the Blog post tool are the three Meta fields that Facebook pulls in when someone clicks on the Facebook icon on a Blog post to 'Share this' on Facebook. Those fields are the Meta Title, Meta Description, and Meta Image.  Any of the three fields left blank, will just not be present in the share.  Facebook no longer just pulls a random image from the post, you need to attach the image you want to use via the Meta Image field.

Please note: the Additional Meta Tags field on a blog post is an optional field for meta tags that don't fit the other meta tag fields above it.  It must be a fully coded meta tag. If in question, leave it blank.

If you have problems with sharing a post, you can go to facebook's debugger and see what the issue is. If you want to change the image that is used in the share post, you will need to ask facebook to rescrape the URL (through the debugger tools).

Check facebook developer tools if you are having difficulty sharing items. There are recommended and minimum requirements for image sizes. As of this post, the recommended size for the image is 1200 x 630 px and the minimum is 200 x 200 px.