WordPress.com does not provide a way to edit code other than CSS. Go to http://en.support.wordpress.com/com-vs-org/ to learn more about the differences.
You can add CSS to your WordPress.com blog if you purchase the custom design upgrade. There is also a way to replace your themes stylesheet completely if you have some CSS you'd like to use to completely replace what you have now. Note that CSS is theme-specific, so if you get a CSS file from someone else and you want to paste in the changes on WordPress.com, then you need to make sure you are using the same theme that the CSS was designed for.