So a nuclear attack has three components to its deadliness. One is the initial blast. Anything at the epicenter is vaporized. Anything within a given radius of the epicenter is blasted away, depending on the power of the weapon. Second, everything catches fire and this multiplies the damage. Third, which is less of a factor now that nuclear weapons use their fuel more efficiently, is fallout. Depending on the amount, it can make entire areas uninhabitable for quite some time. With one or two bombs, as seen in Japan, those areas can be habitable relatively quickly. But, say, total nuclear war? That's an entirely different scenario.

Now, a nuclear attack is likely to be centered around major population centers. You're pretty much screwed if it comes to pass. But if you're far removed into rural territory, you could manage for quite a while given that total war doesn't cause a nuclear winter. The other issue would be the aftermath of such an attack on things like electricity, water sanitation, supply chains for food and supplies, the environment, etc. We could literally bomb ourselves back to the stone age of which the recovery takes centuries.

In short: one bomb? So long as you're a couple feet underground and removed from the immediate area. A full nuclear exchange? You're probably screwed either immediately or eventually.