First of all, do you have a web host server yet? If you haven't, you can get a FREE web hosting at 000webhost.
Now back to the title, as you know co.cc is a free domain as long as your website is for personal purpose. For business purpose, the registration is free of charge but $3 renewal fee will be charged after a year of free usage.
After you registered a co.cc domain, you must setup the domain in 48 hours. Otherwise, they will cancel the domain you registered. Like most of the web hosting with cPanel, I'm using 000webhost as the example.
Choose Name Server (DNS) service type for your domain settings.
Name Server 1 enter ns01.000webhost.com
Name Server 2 enter ns02.000webhost.com and click the Set up button.
Go to 000webhost CPanel, click Parked Domains. Enter your registered co.cc domain and click Park Domain. Your shining new domain will link up with your webhost in no time.
That's how you use your own domain with most of the web hosting servers. The Name Servers are vary in different web host companies to configured and point to their DNS servers.