How can we move our domain name from 1&1's control over to our new host with as little affect (if any) on downtime for our domain name.

We've tried moving name servers before and our site went dark despite us defining all the old records on to the new name server host, now this time we're going to move the entire domain to another company but we've been bit so many times by this that I'm trying to find out what the process should be, and whether it can be done in a way to prevent down time