Midnight here and past my bedtime, but I will see if I can get you pointed in the right direction
First thing you need to do is move your content so you don't need to type it all again, you export from your current blog and import to your blog here: http://en.support.wordpress.com/moving-a-blog/#moving-from-wordpress-org
Once you have the blog here set up the way you want it. Map the domain name you have already bought to your blog here: http://en.support.wordpress.com/domains/map-existing-domain/
Cost $ 13.- / year U.S. dollars
Once the domain is mapped it can take 24 to 72 hours for changes to reach the far corners of the internet, but changes usually start after a few hours.
Once your site is set up here and working with your custom domain name you can cancel your old hosting.
Hosting is free here, but WordPress.COM does from time to time put ads on blogs to pay for the "free" hosting. Some people don't like ads and buy the No Ads Upgrade at $ 30.- / year U.S. dollars
I have the no ads on the site linked to my name, I have a couple of four other blogs that I just accept the Ads and don't worry about them, your choice but did want to warn you about them since they are in the terms of Service.
You be welcome & Good luck with the move
the links below should take some of the mystery out of what you are doing
Support documents & learn WordPress