You can't on a free hosted WordPress.com blog. You will need to hire a web host and set up a WordPress.org install to do that.
You cannot build or use your own custom theme built from scratch at WordPress.com.
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/
If you have CSS editing experience the 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/
Custom Design - Frequently Asked Questions > http://en.support.wordpress.com/custom-design/#frequently-asked-questions
See also > WordPress.com vs. WordPress.org: The Differences > http://support.wordpress.com/com-vs-org/