When creating a new board you will be prompted to specify which membergroups have access to it under the Allowed Groups menu. Simply check the membergroups you want to have access to the board.

The board will only be visible to the groups you have checked, and invisible to all other unchecked groups.

These settings can be edited on a per board basis via the Administration Center > Forum > Boards > Modify Boards, or on a per membergroup basis via Administration Center > Members > Membergroups > Visible boards.