cPanel
cPanel provides a MySQL Database Wizard and this is the easiest way to create a database. You can find the instructions for this in the cPanel Documentation here:
https://documentation.cpanel.net/display/76Docs/MySQL+Database+Wizard
cPanel also has functionality for general care and maintanence of your database. You can find that documentation here:
https://documentation.cpanel.net/display/76Docs/cPanel+Features+List#DatabasesTab
Plesk
Another popular web hosting control panel, Plesk aims to provide all database management within a GUI style interface. To create a new database you would follow the instructions here:
http://download1.parallels.com/Plesk/PP11/11.0/Doc/en-US/online/plesk-customer-guide/65157.htm
Webmin
A third popular hosting control panel is Webmin. You can find basic instructions here:
http://linuxconsultant.info/tutorials/webmin-tutorial/webmin.html#mysql
GoDaddy
GoDaddy is a popular hosting service and they have their own unique control panel system. The current instructions on how to create a database on your website is located here:
http://support.godaddy.com/help/article/36/creating-mysql-or-sql-server-databases-for-your-hosting-account
Warning:
GoDaddy servers do not meet the minimum requirements for vBulletin 5 at this time. Also we recommend not using GoDaddy's Windows servers with vBulletin 5.