If you want to change the blog address ie. the URL starting with http:// then you must be logged in as Admin under the exact same username account that registered the blog to do that by using this guide http://en.support.wordpress.com/changing-blog-address/
Proceed with caution reading carefully each and every step before taking it.
If you want to purchase your own domain then in order to map to a domain one must have an underlying .wordpress.com subdomain blog to map from. If you have registered a .wordpress.com blog you log in under the exact same username account that registered the blog and purchase a domain name by purchasing an annually renewable domain mapping upgrade for the blog. See here http://en.support.wordpress.com/domains/
Dashboard > Store > My Upgrades is where you do the primary blog set up knowing it can take between 24 - 72 hours for domain name propagation to take place throughout the internet. You can view the DNS changes here > http://www.whatsmydns.net/ What's important during that stage is to be patient.