When doing this, the most important thing is to make sure that at
least one of the DNS server listed in all your domain name
registrations is always working during the whole process.
Changing domain registrations and/or DNS server registration can
take anywhere from 12 to 72 hours to be updated on the root servers
etc.
And it could take even longer for the changes to reach the
whole Internet if you current NS-records or associated A-records
have long TTL values.
If you are moving both your DNS servers, if at all possible try
to move only one at a time.
This way your visitors will still be
able to reach your web-sites etc. during the whole process.
Another way to ensure continuous service is to have both the old
and the new DNS server running for several days during the move.
If you are keeping the DNS server name (typically
"ns#.domain.com") and just moving it to a new IP address, then you
only need to change the DNS server registration (ns#.domain.com =
IP) with your registrar and change your own A-record for the server
name.
Changing the DNS server registration is often a "hidden"
function with the registrar.
For example with Network Solutions
you login to your account, and then use the "Manage Host Servers"
function.
Other registrars may call this something else - or
don't even have an online function for this and instead require you
to e-mail them about this.
Keep in mind that if you host domain names under different
registries (for example .com and .co.uk), you will need to change
the DNS server registration with each of these registries.
If you are also changing the DNS server name, then you will need
to update each individual domain name registration to list the new
DNS server name.