Very, very general:
It's all depend on your zone configuration.
If you are using in-bailiwick (the term in-bailiwick means that nameservers for a domain are in the same domain) type of configuation you need to change all your glue records in every domain for the new IP (you change that via your registar).
If you are not using glue records (out-of-bailiwick/glueless) you need prepeare you DNS name for change (lower TTL).
In both cases you should run both servers together (old and new) for some time (it's just good advice and is not a requirement).
Change (propagation) in registry takes from 24 to more hours.