The Internet Archive has this movie in their collections for everyone to download or stream (DivX, MPEG2 and Real formats). I just saw this in full for the first time. Before that I had only seen a part of it in some episode of Quantum Leap (I think).
The film was made in 1951, by Archer Productions and sponsored by U.S. Federal Civil Defense Administration. Run time roughly 10 minutes, black and white.
It has a turtle called Bert, who, of course, ducks and covers masterfully. It shows how to cover oneself in case of nuclear strike: Get under tables or against the walls, away from windows, lie down and put head between legs or agains wall, and protect your neck (this is important). It also shows that even shallowest wall or even the thinnest cloth can easily protect you from the evil and disastrous atomic explosion and fallout.
(Of course, these gimmicks actually work, but that saying these actually protect you enough in a nuke strike is like trying to play a contrabass by blowing.)
Operation Flashpoint: Cold War Crisis tagline gets the point across much more truthfully, of course: "If you see the flash, it's already too late."