How can I set a website image that will show as preview on Facebook?
1. Include the Open Graph XML namespace extension to your HTML declaration
<html xmlns="http://www.w3.org/1999/xhtml"
xmlns:fb="http://ogp.me/ns/fb#">
2. Inside your <head></head> use the following meta tag to define the image you want to use
<meta property="og:image" content="fully_qualified_image_url_here" />
Read more about open graph protocol here.
After doing the above, use the Facebook "Object Debugger" if the image does not show up correctly. Also note the first time shared it still won't show up unless height and width are also specified, see Share on Facebook - Thumbnail not showing for the first time
Note also that if you have wordpress just scroll down to the bottom of the webpage when in edit mode, and select "featured image" (bottom right side of screen).