I believe that getting into project management is in some ways a lot like getting a job in construction, especially in smaller companies or volunteer positions. You simply show up and start doing some work, then the lead guy says "Who the heck are you"? and you say "I'm the guy applying for your laborer job.".
Similarly, you could find your way into a project management role in a free software project by searching for new projects that have one or two developers who seem overwhelmed with feature requests, community outreach, and could use some relationship management between users and development.
Next, just start helping. In every free software project forum, there are questions that get asked over and over again and support requests that are asked over and over again. You could start by acting as a buffer between the developers and the community and slowly grow as the project grows.
You could also organize a timeline based on communications you've seen between developers and community, and you could even help find more volunteers for testing and other tasks that could free up the developers time.
However, to be successful, keep in mind that you are working for the developers and their project and not the other way around. If you try to take over or take the project in a direction not supported by the developers and the community, you will fail.
As a place to start, check out Google Groups. There are all kinds of free and open source projects there at varying stages. Look for ones that are starting to pick up steam and that seem to need some help.