First of all, just in case you are asking What are nameservers? Now that is out of the way.
When creating private nameservers, you must register at least two.
To register private nameservers with GoDaddy, log in to your customer account and follow this guide.
1. Go to Domains and then My Domains.
2. Select the domain you wish to register the private nameservers for.
3. Under the ‘Host Summary’ section, click on ‘ADD’.
4. In ‘Host Name’, enter ns1
5. In ‘Host IP1’, enter your primary IP address.
6. Once you then click ‘OK’, your nameserver is registered
7. To register your second nameserver, repeat the above steps, substituting ns2 as the ‘Host Name’, and when entering your IP address, increase the last number by one. (eg. if your primary IP address is 70.35.90.162, then the IP address for ns2 will be 70.35.90.163).
Note: When creating private nameservers, it may take up to 72 hours for these to propagate throughout the internet.