Many games’ websites (for example the amazing Heroine Dusk as of May 2nd, 2013) miss two minimal elements that make a game’s website more noticeable and sharing it more rewarding to the sharing party: Favicons and preview images.
Favicons help find your website among 10-100 tabs.
Preview images allow users of the social website see content before clicking the link. This is necessary to process the masses of links in Facebook feeds for example. Text gets skipped.
All you have to do is upload a 16×16 image “favicon.ico” and add the following code to the <head> section of all your HTML pages.
<link rel='shortcut icon' href='favicon.ico' />
You don't have to use .ico file format (supported by GIMP). See Wikipedia's How to use Favicons for other formats.
Isn't this better? Even if the icon is ugly, at least it helps differentiate from other tabs.
All you have to do is upload a screenshot of your game "screenshot.jpg" and add the following code to the <head> section of all your HTML pages. Important: the image path has to be absolute, not relative.
<meta property='og:image' content='http://example.com/screenshot.jpg' />
Now the "share" is noticeable in the Facebook/social whatever website feed.
OpenGraph has many more metadata features. For example you can also use og:description to change the text that is displayed by social media sites like Facebook. Images are more important though. Sorry to say.
Still reading? You should add short descriptions of your game to the website title and body. Think about the fact that the <head> <title> element gets displayed as the title in Google search results. Think about how to describe your game to somebody who does not know what your game is or who doesn't know the definition of your game's genre.
What I said above in action
I made a silly game a while ago. The best part about making it was learning about OpenGraph.