Tips for faculty members seeking administrative responsibilities
Don't worry, administrative responsibilities will find you unless you flee them, and even then you probably won't avoid them.  At most universities, young faculty are expressly spared administrative responsibilities so that they can focus on research and get tenure.

If you're really looking for them, generally all you need to do is vocally speak your mind on every issue that comes up.  Most of your colleagues will feign apathy in order to avoid being assigned to a committee.