I don't know of a module that does this for you automatically, but
Facebook has some very limited documentation on how to add the Like Button. The great thing about that page though, is that it has a form that will generate an iFrame for you. I am going to walk you through adding this Like Button to your blog.
Copy the iFrame code you want to use, and make sure that you paste it into a text editor so that you can add a little something to it.
Add the following attribute to your iFrame code: id="ifFacebook"
Remove the href key/value pair from the querystring in the source attribute of your iFrame tag, and add this to the end of the remaining URL: &href=
Finally, place this jQuery snippet below your facebook code:
<script language="javascript" type="text/javascript">
jQuery(document).ready(function(){ jQuery('#ifFacebook').attr('src', jQuery('#ifFacebook').attr('src') + location.href); });
</script>
The final step is to add this to your site. There are a variety of ways to do this. Using a method like PageBlaster would be the closest thing to a "best practice," and you could use the Footer setting in the Module Settings. However, I added this code to the ViewEntry.ascx user control of the blog module, and replaced it on my site. For my purposes, I simply added the resulting code just above the comments and chicklet section in the control.
Here's the example code I ended up with:
<iframe id="ifFacebook" src="http://www.facebook.com/plugins/like.php?show_faces=true&width=450&action=like&colorscheme=light&height=80&href=" scrolling="no" frameborder="0" style="border:none; overflow:hidden; width:450px; height:80px;" allowTransparency="true"></iframe>
<script language="javascript" type="text/javascript">
jQuery(document).ready(function(){ jQuery('#ifFacebook').attr('src', jQuery('#ifFacebook').attr('src') + location.href); });
</script>
You can see an example of it on any of my blog posts, like
this one.