This youtube video shows a Public Service Announcement that was shown at home and in schools to help kids prepare for the imminent threat of a nuclear bomb.
The National Archives brings us a later version and provides an explanation about family fallout shelters. Scroll down to the bottom of the page to find links to presidential Executive Order 10186—Establishing the Federal Civil Defense Administration in the Office for Emergency Management of the Executive Office of the President: https://www.hsdl.org/?abstract&did=464649 and other primary source papers from the Eisenhower, and Kennedy eras.