Manual:MySQL

http://meta.wikimedia.org/wiki/Special:Search?search=database&go=Go

Mysql

Mysql config

Basically, the installation script takes care of everything for you, if you have mysql installed, and you supply the script with your mysql root password, which is by default blank and needs to be changed, if you haven't already.

If you are installing on an ISP you might have to share a db with some other applications, hopefully there isn't conflict between the table names.

Some ISP's allow you to have multiple databases. You might be able to access them through phpMyAdmin or some other web based configuration tool. Some ISP's allow you to have multiple database users, especially if they are using DirectAdmin or similar ISP user interfaces

Maintanance
There are some .sql files in the maintanance directory of your mediawiki installation, you might need to run them if there is ... corruption? or database format change when upgrading.

export db
How to move a MediaWiki Database

docs
http://dev.mysql.com/doc/mysql/en/index.html