How do I redirect my blog posts to a subdomain?

I currently have my blog at alexangas.com and would like to move it to www.alexangas.com.

Is this as simple as changing the WordPress Address and Site Address in Settings? How can I ensure that users hitting alexangas.com/someblogpost are automatically redirected to www.alexangas.com/someblogpost?

Yes. I just did an experiment on my own site to verify that changing those settings will redirect between www and non-www as you specify.