How Do I Edit the Wordpress.com Theme

One of the most common questions that volunteers on the wordpress.com support forum answer everyday is: “How do I edit the wordpress.com theme?”

The answer is:
At wordpress.com we are on a shared multiuser blogging platform. The reason no individual user can be allowed to edit the underlying template for their theme, is that doing so, would likewise effect all other blogs with the same theme.

Can I edit my template?