One of the beauties of blogging is that you can write the content once and then have it distributed across multiple social media channels (e.g., Twitter, LinkedIn, Facebook) automatically and instantly, thereby broadening your audience by many times. Sort of like hub-and-spoke (with the blog being the "hub" of content, and the "spokes" being the various social media channels through which the blog content is fed).
A key tool in the distribution of blog content through social media channels is the RSS feed. For example, LinkedIn has an application that will monitor your RSS feed and add new blog content to your profile whenever your blog is updated.
When it comes to Twitter, there are some blogging services (like Typepad) that will automatically connect directly to your Twitter account via a web services API.
Another option (for those using blog services that can't connect to Twitter via an API) are various RSS-to-Twitter applications that will monitor your RSS feed, and publish any blog updates on Twitter at appropriate intervals.
This December 2009 article on BlogTips does a great job of reviewing the various RSS-to-Twitter tools. Of particular interest was the news that Feedburner (the #1 RSS feed management tool acquired by Google) now offers a tool called "socialize" that will monitor your RSS feed and publish new blog posts to Twitter. Given the efficiency of using a single interface, we're going with Google going forward. But I can say we've had a good experience with TwitterFeed.