are any free database programs that use the mysql platform that I can use to practice building databases.

There are hundreds to thousands of them.

Can you be more specific as to your needs?

If you just want to practice "building databases", you have everything you need within MySQL itself. You can use it to create, populate, modify, and view a database.

It might be useful, as well, to get the MySQL Query Browser and MySQL Administrator (GUI tools.)

Now, if you want to write some program or website that uses MySQL, that's another matter. You need to do some narrowing-down, as I think my fingers would be tired after typing-in those thousands of program names... :)

This will give you all you need to learn to install, maintain, and use MySQL, and learn it's SQL language.

I'd suggest a good book, as well. Since you aren't interested in this point in any specific web technology but in MySQL itself, get one that focuses on MySQL itself, with perhaps some overview chapters on web technology (scripting, etc.) to give you an idea of how it can be used in a website scenario.

I wouldn't get something that focuses on "MySQL and PHP", etc.

I have the DuBois book, and find it comprehensive and understandable.

One suggestion I would make for acquiring such a tome cheaply is to check the "used" section on Amazon and buy from their third-party sellers. You can get all but the very latest books in decent condition for much less money. (I mention that because I notice that that's how I got that book...)