option 1 - purchase a domain mapping upgrade and have your blog continue to be hosted by wordpress.com
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 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.
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.
option 2 - move your blog content into a wordpress.org install
Here is a brief summary of steps we take to move to WordPress.org
WordPress.com and WordPress.org are completely separate.
1. Hire a web host http://wordpress.org/hosting/
2. Set up a WordPress.org install and equip it with a theme and plugins.
3. Export your content out of your WordPress.com blog http://en.support.wordpress.com/export/ and import it into the install.
4. Purchase a site redirect upgrade from wordpress.com
http://en.support.wordpress.com/site-redirect/ or if you have domain mapping then update the nameservers http://en.support.wordpress.com/domains/domain-management/
5. Transfer subscribers and stats. See http://en.support.wordpress.com/moving-a-blog/moving-your-subscribers/
6. Set your wordpress.com blog visibility to private. To change blog visibility to private go to > Settings > Reading scroll to Blog Visibility and choose option 3 . See the guide here http://en.support.wordpress.com/settings/privacy-settings/
Alternatively you can purchase a Guided Transfer and Staff will do the move and set up for you http://en.support.wordpress.com/guided-transfer/