Usually that's done by creating a Role within the Catalog where your cube's in.
Right click 'Roles' and then 'Add Role'.
I just wanna highlight the 'Membership' and 'Cubes' Tabs within the 'Create Role' window. First create a group withing AD for those users that should only have access to this cube and then add that cube to this role.
Go through all the other Tabs and make changes relevant to your environment.