If you are installing a third party script that will connect to mySQL, your configuration script, or web based installer will ask you for certain variables regarding mySQL.
Typically, the first step is to create your database:
Then when you run the installation script, the fields should look as follows:
Please note that the password is the only field that does not require the "username_" in front of it.
"username_" is your cPanel username. You will see the database name and any users connected to that database listed in the database manager after you have completed steps 1-3 above.
Finish your installer or save the configuration file and run your script according to the readme file that was included with the script.
You will get permission errors. You need to make these in the cPanel database manager as outlined above.