More and more software packs will create their own database if installed from Fantastico.
For those that require you to create the database access first then follow these instructions. Login to your cPanel and click MySQL Databases. Follow the on-screen sections - add a name for your database and click create database - add a user and password and click create user. Finally use the drop downs to match a database and user and assign privileges.
After your database is created you can manage it from phpmyadmin. This can be found at the very bottom of the MySQL page.