If you are starting with the Java database ("Derby") which is provided with the standard JDK, you probably don't need to install anything.
If you use another DBMS, go to its website and see what they tell you.
This example for MySQL tells you which connector to download; you would have to download MySQL as well.
[edit]Corrected URL format[/edit]
[ January 18, 2008: Message edited by: Campbell Ritchie ]