Comment Start slow, start small, stick with it (Score 3, Insightful) 282
Vim was sort of a dive-right-in situation. Bram maintains a vast TODO list that ships with every version of the product. I spent a while reading it, picked out a couple things that seemed like they ought to be easy, and got to work. I joined vim-dev and mailed out patches. I didn't do a ton for the app, but I got a few things in.
Mozilla was a different beast in many ways. It was a much more structured environment due to the review process and the presence of Netscape. Also, it was in C++ (which I barely even knew, thanks to some shoddy university training), and not just any C++, but XPCOM. At first I was intimidated by the size of the code and not knowing where to start, so I didn't even touch the code. I spent several months just sitting in #mozillazine and triaging bugs. I dup'd, I closed, I changed to NEW, all that good stuff. Through this, I achieved two important things: I got a much better sense of how the product worked, and I met some of the players involved through IRC contact. By this time I was sitting on #mozilla as well, but I never said a word.
Eventually, I downloaded the code and bought a copy of Don Box's "Understanding COM" for background reading (that book is amazing). From all the time spent triaging, I knew some of the areas where bugs were piling up and nobody was looking at them, so I started there. I submitted a few small patches, had them reviewed, had people check them in for me. The reviews were harsh sometimes, but I was learning a lot. Eventually I moved around a bit and took on larger fixes.
I did this for a year or so before I got too busy with work and dropped out of sight. To this day it was some of the most fun I've had as a coder. For all its flaws (in those days, Firefox was still "m/b", and Netscape ran the show), it was a great project, and some of the people who worked on it were the best programmers I've ever worked with.
So, my advice: start slow, start small. Figure out who you can ask for advice about something. Look for other (non-coding) ways you can help out that will help you get familiar with what's going on. It's worth it.