If you know a little PHP and understand a little about programming, then its fairly easy to jump into programming with the Joomla API! This video covers how to create a module, the easiest of the Joomla extensions to develop, and covers the basics on how you can start to hook into the power of Joomla. The example is creating a Twitter module, which will take a user's public timeline and display it as a list. It doesn't try to be too fancy, but just gets the job done.
Code is available from here with some minor updates from the time of recording: http://www.gnomeontherun.com/resources/joomla/Joomla-Twitter-Module.html. It was created by Gnome on the run.