The free version of MySQL is called MySQL Community Server and current stable version is 5.0.
It can be found here:
http://dev.mysql.com/downloads/mysql/5.0.html
I chose Windows (x86) ZIP/Setup.EXE - around 40MB large.
Just unzip and run setup.exe.
Choose standard configuration and nothing is either hard or takes long time. The only thing might be
However I skipped it.
After that the configuration wizard takes over:
When not sure always go for standard:
This is where you set the password for root user (like sa in SQL Server)
And that's it! It went really fast and no reboots needed.