Facebook share allows you to define certain portions of page preview. You can define them using the following tags:
[html]<meta name="title" content="title" />
<meta name="description" content="description " />
<link rel="image_src" href="thumbnail_image" />[/html]
Here i will show you how to implement a post thumbnail meta in order to show the right image in the post preview.

Those tags go to header.php which defines your page’s styles and meta informations.

1. Open the header.php
2. Paste the following code before <?php wp_head(); ?>
   [php]global $wp_query;
   $thePostID = $wp_query->post->ID;
   if( has_post_thumbnail( $thePostID )){
   $thumb_id = get_post_thumbnail_id( $thePostID );
   $image = wp_get_attachment_image_src( $thumb_id );
   echo "<link rel=\"image_src\" href=\"".$image[0]."\" / >";
   }[/php]
   (Don’t forget to wrap it up with <?php and ?> if it doesn’t exist.)
3. Save and upload the file to your theme directory. Voila!

You can also use my Facebook Meta Tags for WordPress plugin. It automatically inserts related tags to your site.
Don’t forget to put a facebook share button to your site. You can get one here.
You can read more about facebook meta tags here.

Cheers!