3
irmtfan is right on.
After installing the newbb module in the modules admin, the you need to make it available to the anonymous group of users by doing:
Admin -> Groups -> Anonymous users -> and check box the newbb forum module to give them access to read messages.
At this point anonymous can post as well, so just like irmtfan said you need to:
forum admin --> edit forum --> Access Level :registerd users only
Then boom. Anonymous can access/read forum messages, but has to register as a user to participate in the forum discussions.
I hope that helps./