DNS.

You would need to have one of the accredited registars (http://www.internic.net/alpha.html) register the name and point it to the DNS server hosting records for your domain.

If you host the domain name, then it would be your DNS server. If it was someone else hosting it the DNS record, then of course it would be there server.

InterNic has a FAQ of common questions available here:
http://www.internic.net/faqs/domain-names.html

Unless your running some kind of company, I would not use your own DNS for the internet, because then you will have to have it probe for lists of domain to ip?s. That can take time, and space, and its prob not worth it for a single user.

For a compnay the best way is to get a few IP's from your provider then use a service like http://dyndns.org

If you need something personal try http://tzo.com

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