I will copy all the data onto the new server and test it to make sure every is working. Once I'm happy everything is running I will update the name servers to point to the new servers IP. Unfortunately some ISPs cache the IP so may still point to the old server, if this is the case you will be able to access the site via:
http://72.21.42.74
I will put a notice up when the actual move takes place and expect downtime to be only 1 hour.