We cannot access the database for free hosted WordPress.com blogs. To move your content you need to create an XML export file of your content. It will not include the theme as they cannot be exported. See 3 below.
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/
NOTE: WordPress.com and WordPress.org have different log-ins and run different versions of themes with same names. If you don't have a username account at WordPress.ORG click http://wordpress.org/support/ and register one on the top right hand corner of the page that opens, so you can post to the support forums there and receive advice from WordPress.ORG bloggers.