If you own an existing custom domain purchased somewhere else, you can “map” that domain to your WordPress.com site. Domain mapping is a paid upgrade that costs some amount per domain, per year. This fee is unrelated to the amount you pay your registrar for your domain itself. You will need to remember to continue renewing your domain with your existing registrar even after you have mapped it to WordPress.com.
To map a domain to WordPress.com, you first have to make some changes at your domain registrar that will “tell” your domain where to point. Your registrar is whoever you purchased your domain from. It’s not possible for us to make these changes for you if your domain isn’t registered here with us, but if you find the following steps confusing, your registrar should be able to help you out.
Instructions for Mapping an Existing Domain are given further in the article, http://www.elegantthemes.com/blog/resources/everything-you-ever-wanted-to-know-about-wordpress-domain-mapping