You can edit your theme, and add this to comments.php
<iframe src="http://www.facebook.com/plugins/like.php?href=<?php echo urlencode(get_permalink($post->ID)); ?>" scrolling="no" frameborder="0" style="height: 62px; width: 100%" allowTransparency="true"></iframe>
<div id="fb-root"></div>
<script src="http://connect.facebook.net/en_US/all.js#xfbml=1"></script>
<fb:comments href="<?php the_permalink(); ?>"></fb:comments>
it would go just above <div id="comments"> in your comments.php file.
see here for more info:
http://developers.facebook.com/blog/post/472
I used this tool to debug the issue:
http://developers.facebook.com/tools/lint
On Facebook, I found the Apps page. I went into Edit Settings, then Web Site and had to enter my main url, and domain name.
Get the App ID and add this to your header
<meta property='og:title' content='<?php the_title(); ?>' />
<meta property='og:site_name' content='Your Site Name' />
<meta property='og:url' content='<?php the_permalink(); ?>' />
<meta property='og:type' content='article' />
<meta property='fb:app_id' content='Your APP ID'>
That might get you started anyway if you prefer to do it manually.