For those who want to work on existing Gnome projects, it is important to become part of the Gnome community. There are a variety of ways to do this, but the best way is to send me piles of money. However, a more realistic way would be to join the Gnome mailing lists of interest to you (see http://mail.gnome.org; specifically note the gnome-love mailing list), and to assist a Gnome project or two. Even though you may not be able to work on Gnome programs yet, there are a variety of non-programming projects listed at http://developer.gnome.org/projects that you can join and which will benefit you in many ways. For example, helping the Gnome Bugsquad (the project with which I am most familiar from that list) can:
The "support" group advantage I listed above is common to most any of the projects that you could join, but it is one that I believe is very important. There is a lot to learn in assisting a large project like Gnome and it helps to have others that can help you solve problems or answer small questions. During my time with the bugsquad, there were many times (though usually not during official Bug Days) when I received tips on getting garnome or jhbuild to work, pointers to tutorials, learned more about Gnome in general, etc., and there have been many times that I have in turn helped others too. This was not the job of the bugsquad, but it is something that happens often. It is these type of "support" group functions of the various projects that are potentially the most useful, even if they are only side-effects to the main purpose of the project.
Since I am the most familiar with the Bugsquad, let me give a few more pointers about it. I believe that it is a little different from the other projects in that it has been the starting point for many Gnome developers and it is advertised as a great way to start for those who want to become Gnome developers. A good starting point is to read the triage guide at http://developer.gnome.org/projects/bugsquad/triage/. It should contain the other instructions you need for triaging bugs. An alternate starting location is Andrew's guide on testing Gnome. Bug triaging and beta-testing tend to be closely related, though they can be separate. The bugsquad does both activities, though they focus more on helping people learn how to triage bugs. I believe that it is a good idea for those who want to become Gnome developers to spend at least a little time doing both.
Finally, remember that it is human psychology to provide more assistance to those who are helpful, so be someone helpful--even if it means spending some time on non-programming tasks.