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First you go to System Admin - Groups and create a new group.
See this
Faq Page on groups.
Add the users that you want to access the private forum to that new group you just created.
No go to the forum admin page, create a forum, at the top of the page that you create the forum in you will see "Global Access Level:" and a series of checkboxes with your groups listed. Put a checkmark here by your new group to give them access to the private forum. Fill in the rest of this form normally until you get to "Topic permissions for this Forum" at the bottom of the create forum form page. Here is where you set all the permissions for the forum. Give only your new group permissions here, and uncheck the boxes by all other groups.
Now only the users listed in the group you created will have access to this private forum.
HTH.