you will be edit to chance css codes (design) of an existing theme, but not able to upload your own design. Yet, WordPress offers Sandbox as theme, which is a very powerful theme in combination with custom css.
@theutopianpolitico-the site linked to your username isn’t a wordpress.com blog. Just pointing that out. This forum is for users of wordpress.com. If you haven’t yet, read the two stickies at the top of the forum front page, which explain the difference between com and org.
If you are talking about a wordpress.com blog (as I note you are a designer), as thomasrstegelmann pointed out, buying the yearly Custom CSS upgrade allows you to skin a wordpress.com site. Have a look at the Sandbox design competition results. http://sndbx.org/results/designs/ Sandbox10 is the newer version of Sandbox. You can’t modify the underlying PHP or HTML.