Running nameservers yourself.
SHOULD YOU
Usually not. DNS hosted by your registrar or a specialist provider is more resilient, geographically distributed, and free or cheap.
Running your own means your DNS is down when your server is down, which is precisely when you need it working.
IF YOU DO
You need at least two nameservers, ideally on separate networks. Both on the same VPS provides no redundancy.
Register the nameserver hostnames as glue records at your registrar.
THE SOFTWARE
BIND is the traditional choice. PowerDNS and others exist. Control panels install and configure one for you.
THE RISKS
An open resolver, which answers queries for anyone, is abused in amplification attacks. Configure it to answer only for your own zones.
Misconfiguration takes every domain offline at once.
THE PRACTICAL RECOMMENDATION
Use external DNS. Point your domains at a provider, keep the records there, and let your server serve websites.
This also means DNS keeps working during a server rebuild, which matters more than it sounds.