CMS features, including blogging, will not be part of the Muse 1.0 release. We intend to add CMS features to Muse in the future, that will work with Adobe's Business Catalyst platform. BC already has CMS features (seehttp://www.businesscatalyst.com/product-tour/overview for more info), but Muse isn't yet able to take advantage of them natively.
In the meantime, others have had success embedding blogs into their Muse sites. Take a look at the Jam Session Dani hosted for more info on this:
Embedding and Styling Blogs / Recorded Wednesday, February 22 (2nd from the bottom)
http://www.adobekb.com/events.html
