You cannot remove footer credit links on any blog hosted by WordPress.COM. There is no upgrade that provides that ability. The only theme you can use are here https://wordpress.com/themes/
Removal of footer credit links is a Terms of Service violation. Though removing footer credit links, which leads to the untrue assumption that you designed the theme, and that you are hosting your site yourself is not allowed, it's possible to add your own text to the footer area using CSS if you have purchased the Business bundle or Premium bundle of upgrades containing the Custom Design upgrade. Then you can include styling credit if you have done any unique styling and/or include a copyright notice.
http://en.wordpress.com/tos/ 11.
http://en.support.wordpress.com/custom-design/#frequently-asked-questions
http://en.support.wordpress.com/custom-design/
http://en.support.wordpress.com/custom-design/editing-css/
http://en.support.wordpress.com/custom-design/custom-fonts/
If you want to add to the footer using CSS editing please use this link http://en.forums.wordpress.com/forum/css-customization#postform so you can copy and paste your text into a thread that will appear in the CSS Forum where you will get the help you need.
Added info:
If all you want to include is a copyright many bloggers do that by including a copyright notice in a text widget.
http://en.support.wordpress.com/prevent-content-theft/#1-include-a-very-clear-copyright-notice-on-your-blog
Some like myself link that text widget notice to a copyright page like this one http://onecoolsite.wordpress.com/copyright/
http://en.support.wordpress.com/widgets/text-widget/