You need to have admin/coordinator role to archive/unarchive client or staff. Please see Roles for further reading.
Archive: In order to archive staff, navigate to left hand side menu. Go to "Staff", then "List". Click the staff you want to Archive. Once you are at staff detail page, hit "Archive" button located at the bottom right of the page (See below).
Unarchive: In order to unarchive staff, go to "Archived" tab under staff (located at left hand side menu). Go to staff who need to be unarchived. Hit "Unarchive" button which can be found in front of the staff. Now staff is unarchived and he can be found in staff list page.