I have a MySQL server on my Scientific Linux 6.2 system. Right now I know how to create a new database, and set up users.
I need to setup LibreOffice Base to connect to the MySQL server, via either ODBC or JDBC (ideally over SSL).
How do I do this? Do I need to install anything on the server to allow this to happen?
All you need is MySQL using sockets and the appropriate connector (downloadable from the MySQL site). After that it's just a matter of configuring the DSN. If you have questions relating to that I suggest you first read the documentation and then ask over at SO if you're still stuck.
It's easier to maintain a machine if you use distribution official packages. There are official mysql connector packages in Red Hat Enterprise Linux so I guess they are part of scientific linux too.
wrt SSL, you can take a look at the official doc: http://dev.mysql.com/doc/refman/5.0/en/connector-j-reference-using-ssl.html