When creating a new board you will be prompted to specify which membergroups have access to it. Check the boxes next to the membergroups that you want to have access to the board. The board will only be visible to the groups you have checked.

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.