In order to map to a domain one must have an underlying .wordpress.com subdomain blog to map from http://en.support.wordpress.com/register-a-blog/ and the domain name you desire must be available for purchase, or you must already own the domain URL.
After you have registered a .wordpress.com blog you log in as Admin 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 from the blog's dashboard at > Store > My Upgrades.
See here if you do not own a domain http://en.support.wordpress.com/domains/
See here for mapping an existing domain that you already own http://en.support.wordpress.com/domains/map-existing-domain/
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.