1 - set domain to new account
2 - upload the latest file package for your cms
3 - install latest package
4 - upload your backup files for any non-standard install modules/blocks etc
5 - with phpmyadmin or whatever your host is using for your database, overwrite your new one with your backup
6 - remove any install specific files
Things to be aware of - be sure to use the same database prefix when installing the fresh db as your backup used. Double check file permissions and that should be it.
I move postnuke installs around all the time and that's how I do it.