Staging site is the one that you’ve been developing as a redesign of the live site, that has been active till now.

1. Install Duplicator plugin on your staging site and run a full backup generation with it. Ignore warnings on the scan step, in most cases they are related to big files, big overall size of the site or other things that are not lethal.
2. Make a backup of your live site (either by using Duplicator, or any other mean that you are comfortable with).
3. Create a new database from cPanel of your hosting, create a new database user, and add full privileges for that user on the database you just created.
4. Move the contents of your live site to a hidden subfolder (e.g. oldsite) and then copy your staging site package and installer.php that you got from Duplicator in the main folder of the live site.
5. Access your site on http://yoursite.com/installer.php and follow the instructions, using the credentials of the newly created database and user when requested by the installation wizard.
6. After finishing with installer.php, you should be done with the migration.