Additional information and links:
You can post a Facebook badge in your sidebar. http://en.support.wordpress.com/facebook-badge/
You can use the Facebook liebox widget found here > Appearance > Widgets
You can also enable sharing buttons on your posts, pages and index pages.
Also note the “like” button.
You can have both Facebook like & share buttons on your posts.
You can set up Publicize and publish to your Facebook profile page > http://en.support.wordpress.com/publicize/
Alternatively you can use Networked Blogs http://www.networkedblogs.com/ or RSS Grafitti http://www.facebook.com/RSS.Graffiti for posting to Facebook walls if you prefer. RSS Graffiti periodically checks the RSS/Atom feeds that you specify and posts any new entries it finds to the Facebook Walls that you specify. You can get any feed written on any wall (Facebook Profiles, Fan Pages, Groups, Events and Application Profile Pages). In fact, multiple feeds to multiple walls. You choose the combination.
You can use a Twitter widget > http://en.support.wordpress.com/widgets/twitter-widget/
You can post a twitter follow button > http://en.support.wordpress.com/twitter-follow-button/
How to Add a Tweet Button With Your Twitter Username into WordPress.com http://wp.me/p1gGsz-cn