For the v1.0 of the Blog there is an add-on widget which makes embedding addthis.com toolbars possible. These toolbars provide customizable social sharing buttons to many websites.
This add-on is free and available to Blog customers upon inquiry.
In the Muse Blog v1.0, the toolbar needs to be either manually embedded into each post on which you wish to show that toolbar, or can be placed somewhere on the entire page with our custom widget for refreshing it to share the respective URL of the post the visitor is currently on, instead of sharing the blog's root URL.
For the soon available updates we will provide easier solutions to embed such functionality at the bottom of all posts at once, without the need of embedding one by one. However the first workaround (as described above) is already functional now and available via the "addthis refresher" widget, which as said is free and available to Blog customers upon inquiry.