Finding an open source project to contribute to
The sheer number of projects out there is quite intimidating. I looked on www.ohloh.net which allows nice sorting and filtering but it's not easy to see which projects would welcome a newcomer, or projects which have some straightforward introductory bugs to fix, or even docco to do.
Answer
More than anything, I'd start by building something (a website, an application, etc.) using open source software. If you keep at it, you will inevitably run into issues that warrant fixing or otherwise contributing back. If you run across issues that are beyond your skill level, keep track of them for later, once you've built your skills.
You can also look for projects that have a contributor's guide. Look for @todo comments in the source code, for pointers to issues you may be able to resolve.
Check out the sites for the Google Summer of Code and Google Code-In. There are lots of publicly available proposals for those programs that may provide some inspiration. The open source projects that participate have to apply, so they're definitely projects that are open to new participants.
Look for IRC channels dedicated to your favorite projects and try to help other users there. Ask in the channel who needs help on their project.
The FLOSS Weekly podcast highlights different open source projects each week and they regularly ask guests where their projects need help.