You would want to zip up your ‘lists’ directory, move it, and then unzip in it’s new home.
If you can access your database from the new location, no moving of the database is needed. If you can’t access it, you would want to do a backup of your database, and move it to the new location. Then restore your database, create the phpList database user and password, give it permissions on the database.
Go to the ‘settings’ page on the web admin interface, and change the domain values towards the top of the page, and also verify that all the references to the old domain are changed to the new domain (unsubscribe page, etc… further down the page).
Then you can send yourself a new test email or test campaign, and verify that you did not miss anything.