To manage how your pages are shared on Facebook by users, Facebook has created Open Graph Tags (e.g. article).
For example, you have to add in your site these tags in the head:
<meta property="og:type" content="article">
<meta property="og:description" content="....">
<meta property="og:locale" content="en_GB">
<meta property="og:site_name" content="...">
<meta property="og:image" content="...">
<meta property="og:url" content="...">
In this way, Facebook loads this information to create a Post or Like.
You can find several extension in JED's Social Share category, that can provide a straightforward method to generate the Open Graph Tags for your site.
Similarly, Twitter has also created TwitterCards tags (e.g. summary-large-image)to support the very same functionality (and there are extensions already supporting TwitterCards).
<meta property="twitter:title" content="...">
<meta property="twitter:card" content="summary_large_image">
<meta property="twitter:image:src" content="..">
<meta property="twitter:creator" content="@...">