Most, but not all, domain name registrars include DNS hosting service with registration.
DNS can also be self-hosted by running on generic Internet hosting services.
A number of sites offer free DNS hosting, either for second-level domains registered with registrars which do not offer free (or sufficiently flexible) DNS service, or as third-level domains (selection.somedomain.com).
Free DNS typically includes facilities to manage A, MX, CNAME, TXT and NS records of the domain zone.
Free DNS service providers can also make money through sponsorship.