If you are new to databases, you must start from learning the theory of designing a database for a real life problem. It is interesting but not thrilling, though:
http://searchoracle.techtarget.com/tutorial/Learning-Guide-RDBMS-fundamentals
I won't advise "play around and learn" methodology because it only works with terribly simple concepts such as games but certainly not with databases.
Once you know how to design a database, you will be able to create examples using Microsoft Access that comes bundled with Microsoft Office. A good free alternate is OpenOffice.org software called "Base".
Once you know how to create tables, you need to learn SQL programming, which is luckily a very simple language. It stands for Standard Query Language. Here is a link for that:
http://www.sql-tutorial.com/rdbms-and-database-tables-sql-tutorial/
Although paper books are better than computer screens for such brain-intensive activities.
Once you can write simple SQL statements, you would like to try real programming but my gut feeling says you won't like that because it is a G-damn time consumer. You still can post another question when you reach there.
Good luck.