The only themes we can use are those found here > Appearance > Themes
This is a multiuser blogging platform. There is no FTP access to free hosted WordPress.COM blogs and we cannot install themes or individual plugins into them Those found on the internet are for WordPress.ORG installs which run on different software.
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. http://en.support.wordpress.com/custom-design/custom-css/
If you have CSS editing experience and are willing to purchase an annually renewable CSS upgrade, 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.
If you wish to have complete control over a blog, the ability to upload themes and plugins, and to edit themes and templates then your option is to hire a web host and get a free software install from WordPress.ORG and self host it.