An easy way to get started is "Bugs Ahoy", a Bugzilla search engine that lets you search by programming language and feature area among bugs tagged as "good first bug" with a Mozilla mentor's contact info:

http://www.joshmatthews.net/bugsahoy/?unowned=1

Thank you for this link. I wanted to help Mozilla for quite some time but didn't know where to start, this should simplify things a lot.

We're waiting for you :)

Ideally, the best place is irc.mozilla.org, channel #introduction.

Again, thanks for this. I've intended to get involved but never got around to figuring out how. Having this run across my screen motivated me to get a nick registered, and say hello in the channel.

Same here. I'm willing to use my next "funemployed" round for getting involved. Maybe even writing my master thesis on a mozilla project. I really like how the employees can work from everywhere, also it doesn't have the touch of selling your soul, because they help the world with their work.

They have a great work environment and a good culture, if the nature of the projects is a fit for your personal style. If you thrive in more team-oriented environments it may be rough for you - Mozilla runs more like a big open source project with salaries.

Mozilla folk were very positive and welcoming when I made (minor) contributions to the Core code. The whole code was easy to set up and run on my system too. Just go for it and start contributing!

This is a great place to start: http://www.mozilla.org/contribute/

You should really check it out. Try contributing on a few easy bugs, get an idea about the people involved!