The instructions in the Jetpack blog post about moving the buttons indicated that one could put them in the header or footer. If so, what would they do on a site's homepage?
The buttons can be moved around within a WordPress loop, to display the buttons above the post content, for example.
The sharing buttons were designed to be used on a Page or a Post. Your home page can be considered a Page if you use the front page setting. If you set up your site this way, you will be able to use the sharing buttons on your home page.