To setup remote access to your MySQL database(s) you will need to add the IP address you will be accessing from to the access hosts section under MySQL Databases in your cPanel control panel.
If you will be accessing from your home computer using MySQL database manipulation software you will need to find out the IP address to your local machine, use the following link to check this now: http://whatsmyip.net
If you are connecting from another server you will need to add that servers IP address into the Access Hosts section, you will need to ask your server administrator for the IP address for this.
Now you have your IP address, login to your cPanel control panel and go to the Databases section and select the Remote MySQL option. Now add your IP address using the form provided. Now you have added your IP address you should be able to access your database remotely.
Setup the software to connect to the IP address shown in your cPanel or your domain name on port 3306.
You may need to remove and recreate your database user once you have added your IP to have the users permissions update and allow the remote connection.