This is done with the permission system. We have a complete example of a forum in the demo package of eZ publish, this shows how you can set up a forum. To extend this to require user registration for posting you need to change the roles for the anonymous users, they must not have permission to post.
The registered users will default be created in the guest account user group, this group needs to have a role assigned. This role needs to have permission to create a foum message. Doing this you will get a forum like we have on here on ez.no.
