Add yourself to the Member list
Well, the first thing you can do is introduce yourself and let people know what you're about, and what you're interested in. The best way to do this is to add yourself to the All Members list. Since you've read the FAQ, you know that everyone participating is a member, so adding yourself to the list is the first thing to do. To add yourself you simply edit the wiki. To do this first you will need an account, which you can get by clicking the 'log in' button on the upper right hand of this page. If you don't have an account it will take you to the page to create one. For more information about using a wiki, see Help:Contents.
Join the OSGeo Main site
Unfortunately we don't yet have integrated single sign on for wiki and the main site's infrastructure. So if you don't have an account on the http://osgeo.org main site, then you'll have to create one by clicking on the 'register' button in the upper right. After you do this you'll be able to join projects and email lists and post to forums.
Find a project to work on
The easiest place to start is the Volunteers Needed page, as projects will put up their requests of what they're looking for. You also can email the discuss list directly to let people know what you're interested in, and where you could slot in. You can also go to the [project page] which links to projects and committees that are fully started. After you click on a project you'll be taken to their main page, where you can click to watch the project or request a project role, if you are logged in. You can also browse the mailing list archives, and join any of the mail lists. For more information on using the main OSGeo site, see the Collabnet FAQ
Join a mailing list
On many projects there are 5 or so mailing lists. The best email list is often named the same as the project (like email@example.com), or sometimes discuss. Some lists can be avoided at first, like commits, cvs, and issues (which are automatic email lists from the source repositories and project trackers). The announce will generally be low traffic. The dev and users list may have good traffic if they are programming projects, in which case the users list is probably the place to start. Jump on a list for a project and introduce yourself, ask where you can help out.
Jump on IRC
Many of us hang out on irc, at irc://irc.freenode.net#osgeo. Or in more verbose terms, on the osgeo channel of irc.freenode.net. There are a variety of IRC clients, if you're running firefox ChatZilla is very straightforward. There are many others as well (I use ChatZilla, could someone else add links to their favorite clients?). With IRC you can informally get to know people, what they're working on, and how to help out.
Hack on the wiki
This wiki is where a lot of action takes place. Collaboration is much easier here, so we'll start up new documents here, and transition them over to the osgeo site when we're happy with how they look and what they say. Documents on osgeo.org reflect OSGeo's positions, while on the wiki we work out what those positions are. You can find out where the action has been on the wiki by clicking on Special:Recentchanges. Feel free to add new pages, propose new projects and ideas.
Start a project
Looking for an issue that you feel is very related to the OSGeo effort, but unable to find it? Well then start up a committee. Anyone can take a leadership position in this foundation, it just takes a willingness to dive in, do some solid work, and lead others. The first step would be to email the discuss list to see if the issue has come up before. If it hasn't, then start a wiki page detailing what you think about it, and what a committee would do. Then you can ask the board (firstname.lastname@example.org) to have a look at it, and they will hopefully approve it. This will be easier if you have others who are willing to work on it.