To be clear about this you cannot build or use your own custom theme built from scratch at WordPress.com. There is no FTP access and we cannot upload any third party themes.
The only themes we can use are those found here > Appearance > Themes
This is a multiuser blogging platform. All blogs wearing the same theme are using the same underlying template and we cannot access the underlying files and edit templates or themes. http://en.support.wordpress.com/themes/editing-themes/
There are two free themes, Sandbox and Toolbox designed to allow maximum flexibility for CSS editing and creating new “skins”. Toolbox is more modern and includes a lot of support for CSS3 and HTML5, so it is really only limited by your skills and knowledge.
If you have CSS editing experience the annually renewable custom design upgrade will allow you to stylize the appearance of themes you find here > Appearance > Themes, but will not allow you to change the functionality, by editing the underlying template. It does not allow you to remove footer links to the theme designer or to WordPress.com. Also note that CSS is theme specific, so you cannot use the CSS stylesheets from other themes with the themes at WordPress.COM. http://en.support.wordpress.com/custom-design/custom-css/
See also > WordPress.com vs. WordPress.org: The Differences > http://support.wordpress.com/com-vs-org/