Try your site in this facebook debugger tool. It will tell you what is missing.Eg. below in page head
<meta property="og:image" content="[url to image]" />
<meta property="og:title" content="[page name]" />
<meta property="og:description" content="[content description]" />
There are different ways depending on how your site is built. Eg. This Wordpress plugin creates a link for each image on the page so you can chose between your logo and any other post image on the page. Update 2017: It is now recommended to register a Facebook App ID for your site otherwise the debugger will give you an error. More tags and info