No, there is no additional charge. Whoever registered the domain owns mydomain.com and the use (or non-use) of sub-domains is a DNS consideration only. Many of the web hosts give you a screen where you can do this yourself, so if you have access to the domain management screen, just look for a screen that allow you to create DNS entries (they also control the MX record, for email).

The domain name is registered somewhere. Some registrars provide DNS hosting as well; some go all the way to web site and email hosting. On the other hand, one might register the domain one place, but use somebody else's domain name servers (DNSes), and still a third party's web site hosting. (That is foolish, but people do it).

DNSes are on individual servers (minimum two); web sites are on their own server (usually). These days they may all be on the same physical machine if one is using virtual machine software.

Look at the domain registry information. Network Solutions' whois will pick it up from almost any registrar, so you can use them regardless of where the domain is registered. The domain listing will show who the DNSes belong to. In large companies, both the DNSes and the web sites are typically in-house. Most smaller companies registered at "major" registrars use the registrar's DNSes and often their email services as well.

Most of the "lesser" (forgive my bias) web hosts register their domains with one company and then manage the DNSes and web sites themselves. They often don't automatically define your web site both with and without www, but I can't imagine they would charge you to do so. Where the DNS is in-house, often the technical people aren't sufficiently web knowledgeable to know to define both (and, as I said, some screw it up royally by making one of the two the internal network name).

So, bottom line, no cost should be involved unless whoever is hosting it charges you for everything!

Furthermore, if the setup is not easy to manage you should look elsewhere for services. The difference between $2.99 a year, or $9.99 a year or even more should not be a consideration. You want near 100% uptime plus ability to manage everything yourself without standing on your head. If the current setup doesn't allow that, they should move. It can be done inexpensively.