Over the course of the Cold War, many countries adopted programs for mitigating the effects of nuclear war and attempting to insure survival beyond one. The two main areas here are Continuity of Government (COG), in which a nation tries to assure it will be politically viable after a nuclear attack, and Civil Defense (CD), in which a nation tries to mitigate the short- and long-term effects on a populace. Examples of the former include the Raven Rock ("Site R") facility in the USA, where a "shadow" Congress and Executive Branch, as well as military operations could be housed under a mountain. Examples of the latter include attempts to inform people about the various techniques that might mitigate blast damage ("Duck and Cover" in the early 1950s), fallout avoidance (e.g., fallout shelters in the 1960s), and organize various functions of society for the possibility of rebuilding (which covers everything from restoring the food supply to disposing of millions of corpses). You can think of COG as the plans the government took to save itself from the war, and CD as its attempt to help their citizens survive. They are very different problems because of the vast differences in numbers of people.

Now how effective these plans would have been depends on who you ask and when you ask it and where you're asking. For the continental USA, the early Cold War was much better than the later Cold War; for Western Europe, the prospects of survival were pretty grim from the 1950s onward. The Soviet Union had its own plans of this sort, too, to various degrees of confidence and effectiveness. It is unfortunately very easy for people to dismiss all such actions as silly or pointless or ridiculous — much of the literature on these things is marred by the assumption that it is all "crazy," which aside from not being an entirely technically accurate way to look at it (I mean, maybe it is indeed "crazy" to plan for the deaths of hundreds of millions of people, but the idea that such efforts would be totally fruitless is not correct) is not a great way to think about historical actors (they were not irrational people). In the 1980s, CD became extremely politically controversial in the US and Western Europe, and that controversy has by and large continued to taint how many people, including historians, view and talk about this history.

It's hard to generalize all of such plans into one short answer, given the number of countries involved and the way in which these policies changed dramatically over the decades (in pace with changing technologies and strategies), but the above is an overview. In the US case, for COG, Garrett Graff's Raven Rock is supposed to be quite good though I haven't gotten time to go over it yet. For CD, there are several books of varying quality; Rose's One Nation Under Ground is probably the best of the bunch so far. A comparative study of Soviet and US CD is coming out later this year by Edward Geist, and it should be very good (I have read the dissertation it was evolved from).