Facebook uses what's called the Open Graph Protocol to decide what things to display when you share a link. The OGP looks at your page and tries to decide what content to show. We can lend a hand and actually tell Facebook what to take from our page.
The way we do that is with og:meta tags.
The tags look something like this -
<meta property="og:title" content="Stuffed Cookies" />
<meta property="og:image" content="http://fbwerks.com:8000/zhen/cookie.jpg" />
<meta property="og:description" content="The Turducken of Cookies" />
<meta property="og:url" content="http://fbwerks.com:8000/zhen/cookie.html">
You'll need to place these or similar meta tags in the <head> of your HTML file. Don't forget to substitute the values for your own!
For more information you can read all about how Facebook uses these meta tags in their documentation. Here is one of the tutorials from there - https://developers.facebook.com/docs/opengraph/tutorial/
Facebook gives us a great little tool to help us when dealing with these meta tags - you can use the Debugger to see how Facebook sees your URL, and it'll even tell you if there are problems with it.
One thing to note here is that every time you make a change to the meta tags, you'll need to feed the URL through the Debugger again so that Facebook will clear all the data that is cached on their servers about your URL.