While looking at any page in the CommonSpot dashboard, click on the "Admin" button in the full-width toolbar and choose "Subsite Administration...".
Observe the Select Subsite lightbox; by default, the subsite containing the page you were looking at will already be highlighted; if you want a different subsite, scroll and click on the [+] as needed to see the subsite or sub-subsite you want to work with; click on that subsite, so it is highlighted; click on "Next."
Click on the heading "Security" in the left column.
Click on "General Security" or "Content Security," as appropriate.
Find the check-box with the title "Inherit Security From Parent"; if it is not clear, you can click in it to clear ("un-check") it. That will display the list of groups or users with specified access, matching what the list and access for the parent, but now you can change this subsite to be different. Click on the pencil at the right end of each line to inspect the specific permissions for that user or group:
The group, "Anonymous," means any user who has not logged in (the general public).
Inspect the current settings, and change those that do not match your needs; for example, you might make the changes needed to restrict access. You can return to this dialog later to make changes.
When done, close the lightbox.