Hi JB,
This is really a pretty broad topic and there is not really a quick answer to your solution. Basically MySQL is a relational database system that lets you use SQL to create and use your database. To use MySQL in the broadest sense such as running queries, managing users, and creating databases, etc, you would either have to connect to the mysql server via command prompt or use one of many GUI tools that are available for accessing MySQL. My favorite tool for accessing MySQL is called SQLYog, this tool is very powerful and lets you basically manage anything with your MySQL database.
In terms of your gaming ladder software, odds are there is a setup script or a .sql file that will have all the queries needed to create the database for your system. You should just need to run that script and it will take care of the rest.
Overall though I would really recommend reading up on what MySQL actually is, and what it is about before you get into trying to setup specific databases, accessing it, etc. Here are a few links for you to check out -
http://dev.mysql.com/doc/refman/5.0/en/tutorial.html
http://dev.mysql.com/tech-resources/articles/mysql_intro.html
http://www.tizag.com/mysqlTutorial/
http://www.tutorialized.com/tutorials/MySQL/1
http://webyog.com/en/
Hope this can help
Joe