DNS move, looking for confirmation

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http://www.linuxquestions.org – I have a DNS server at an old companies place and that box will be losing it's IP. The whois record for the domain goes to godaddy which has 2 'A' records; ns.domain.com ns2.domain.com which point to the current 2 DNS servers. Now if I have a new server up and running and the zones copied over, do I just need to change the 'A' location for ns.domain.com to this new IP? I remember back in the day you had to 'register' the nameserver with the registrar, etc. I haven't touched this stuff in a while, and before I go and change the IP of the nameserver, want to make sure all is in check. Thank (HowTos)