1. backup all your config files(apache, dns, etc)
2. gzip all your data then wget
http://oldserver.com/file.tar.gz in the new host. extract the file.
3. set up new host with config files.
(install softwares, setup APM, config httpd.conf with new IP addresses, etc..)
4. change nameservers.
if you going to move to managed host. just ask your new provider. they will do it for you.