A domain name is made up of three parts. In the example of "www.mydomain.com", "www" is known as the "host name" or sub-domain. "mydomain" is the domain name, and ".com" is known as the "top-level domain".
The exact cost depends on what top-level domain you choose.
Domain names are registered with "registrar" companies; Spartacus Systems will be registering your domain name with such a company and registrars charge an annual fee for a domain name.
This yearly fee is pretty cheap. Though the exact cost will vary, plan a "worst case scenario" of $15 per year (the actual cost will be less than that).