DNS assigns what IP address the domain resolves to. The DNS is generally set in the domain control panel of the registrar.
To change the DNS of the domain to point to new hosting, you’ll need to access this control panel (unless the domain has external nameservers which you have access to), if you are not in touch with the original registrant this may not be possible.
You’d be better off initiating a domain transfer as there’s no guarantee the original registrant will continue to pay for the domain and it may lapse.
If you initiate a domain transfer, the registrar will contact the original registrant to confirm their permission, which again may be an obstacle if they don’t respond to the registrar.
It’s also possible to regain control of a domain by contacting the top level authority for the relevant type of domain e.g internic for .com, nominet for .co.uk and going through a process of authentication if necessary.
Great answer - but note that the DNS redirection is done on the REGISTRAR’s control panel which you’re not likely to have access to so you’re constrained to follow EastCoast’s process.
Domain name transfer is about when you are changing your domain name registrar.
That might take up 5 business days. Be informed that while domain name transfer you can keep your DNS settings as they are.
Changing DNS - as usual that is used when you need to change your web host.
But some people think that when they change web host they need to change domain name registrar.
That is not a must.