I'll preface this by saying that this is the bootleg way to add the button; I'm sure there's a better way to do it so people can like individual posts rather than the whole blog. But until Blogger or someone else posts those instructions you might want to try the new "like" button feature on your Blogger blog, so here's an easy way to do it.
- Go to Facebook's developer documentation site's social plugin section
- Put your blog's url into the "URL to like" generator and click "get code"
- Copy the iframe code
- In Blogger, go to Customize and click "Add a Gadget" on the sidebar
- Voila! Now people can "like" your blog, which means that your blog's url will show up in their activity stream on Facebook