To do this, you need your link to have an image in your content. Facebook automatically takes the image in the content of your page and attaches it to the display of your fb post.
But you can also change the image, facebook gives you that possibility too.
It happens that if it is a blog post, it looks like there is a cache or facebook or the blog server that, when trying to post to facebook immediately after posting, it does not recognize the image, having to wait a time to publish.
But having the image recognized, you can either keep it or change it too, at your discretion.