How do I delete the blog so that I can use my domain to build a website using wordpress?
If you already own a domain then you can purchase an upgrade to map from your http://raleighyouthapri.wordpress.com/ site to it.
Read first please http://en.support.wordpress.com/com-vs-org/
Note that WordPress.com does not accept domain transfers but mapping an existing domain is possible.
Domain mapping of an existing domain URL that you already own and purchased elsewhere is not done free of charge. You will have to renew the domain name purchase where you made it and the domain mapping purchase here every year.
Important Notes Before Upgrading http://en.support.wordpress.com/domains/#important-notes-before-upgrading
Mapping an existing domain costs $13. annually. In order to map to a domain one must have an underlying .wordpress.com subdomain blog to map from and it does not matter what that underlying .wordpress.com URL is. It does not have to match the domain URL. 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 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.