First, you will need to access your server via FTP.
Once you've accessed your server via FTP, navigate to /var/www/html
This is your default directory for your WordPress application. You'll want to download or save the wp-config.php file on your server – this file is important!
You'll need to have the files/directories from your current WordPress installation so that you can upload them all (but the wp-config.php file) to your new server under the /var/www/html directory.
Any instances where the FTP software requests to overwrite, select to do so for all instances of your upload.
You'll be importing your current MySQL database to the database named appdb on your WordPress Application server. To do so, upload your backed-up database to the root directory of your server. This can be done via FTP. Navigate to your server's /root directory and upload your backed-up database.
From there, you'll run the following command on your server in shell:
mysql appdb < YourMySQLDataBase.sql
As long as you've ensured you did NOT overwrite your wp-config.php file that came with your server, you should be done!