It's a little difficult and not something I would want to do mid-semester. If you have your own domain then changing wil require a 2-5 day wait for your domain to transfer to your new host - usually only 2 but sometimes longer.
I would just install moodle as normal at the new host. backup and restore each course with all user data into the new host installation and then redirect you students to your new host.
Installing and upgrading help
Somewhat off the beaten path...
This discussion has been locked so you can no longer reply to it.