The countries with nuclear weapons are India, Pakistan, North Korea, UK, France, US, Russia, China, and possibly Israel.
If the UK, or France does it, they'd be utterly destroyed. Their main allies are NATO, the US, and its allies. And if one of them nukes the United States... all of those allies are turned against them. War would be declared, and it would be the US and all but one of her allies vs one country. I would say, odds are, the one country is completely and totally destroyed. Then, the US would probably treat it like it did West Germany or something. It would probably recover (look at Germany today; and this time there wouldn't be a Communist part), assuming the US managed to win without nukes. With Israel, I'd say it is a fairly similar story. The Arab world would love to have the opportunity to destroy Israel. If Israel nukes the US, and suddenly the entire western world is at war with Israel, they would join in. The US probably doesn't want to launch a nuclear weapon at such a small nation surrounded by its allies, and there wouldn't be much of a purpose. I really don't think Israel could possibly fend off the armies of the entire world simultaneously all with complete sanctions and without US aid.
The US would probably want to avoid using nukes back if they can. Many of the US allies would be the offending nations' next door neighbor. Besides the possibility of a nuclear winter.
If it were Russia, China, India, Pakistan, or North Korea, that would be a different story. Actually, with North Korea, it would be a similar story. The US and allies would declare war, and lose all of its allies. But then, there would be a massive refugee crisis, and instability within North Korea. The US could probably handle this, but only after a long time, and not without casualties. I would imagine it being like Afghanistan or Iraq. Again in this situation, the US would want to avoid nukes. There are 195km between Pyongyang, the most likely target for a US nuke in North Korea, and Seoul, a heavily populated capital of a major US ally. So, I would say this one avoids nukes.
If India did it, the effects would be devastating. First of all, global sanctions would cripple the economy. Then, I would guess pretty much the whole world would declare war. It would be a long, hard battle filled with casualties, but I can't imagine India winning. Besides, in this scenario, India may well be nuked in response. Ultimately, I would say this is a lose-lose scenario no matter what, but militarily, India vs the US, NATO, other US allies, and probably Pakistan would not be so good. If Pakistan did it, it would probably be pretty much the same story.
With China, the west just has to completely cut off all trade. China's economy would collapse. But, China is still powerful militarily. In this scenario, WW3 would ensue. China would be nuked in all of its major cities. Forces would completely destroy it. China would become a wasteland, and we'd almost certainly have a nuclear winter. But, while we'd likely win, this victory would not come before China nukes a few major cities. Not good for anyone.
With Russia, it's more complicated. Iran, Syria, North Korea, and some former Soviet states may stick with Russia despite their rogue actions. Russia has more nukes than us, but when you combine our arsenal with that of our allies, we may not be at a disadvantage. World War Three would absolutely begin, no matter what. There would be a massive war. There's no way to avoid nukes in this one. Russia would nuke even more of our allies' cities (and ours, of course) than China. This would be the worst war in the history of the world. In the end, billions (yes, billions) would die, the world would suffer extreme pollution, and the only survivors would be in remote regions or neutral nations. If humanity lives, it would be set back in terms of development by hundreds of years.
If Iran got weapons and nuked us, I would imagine that Russia would stay out of it, especially if our relations improve under Trump. So Iran would be the next Iraq, except with nuclear weapons and more people. It would be a difficult, long, costly war to fight, full of casualties, but there's no doubt that the world would destroy Iran if they launched a nuke.
I'd imagine that, no matter who is president, the above would be pretty much the same, unless our candidate supported the enemy. Trump, no matter how much you may hate him, and even if Russia helped him, would not side with anyone if they nuked us. Russia did want Trump to win, and may have fed data to Wikileaks, but I would guess that was because they hated the treatment they received from the Democrats, and thought Trump may be more friendly to their interests. Saying that Trump is a Russian spy is entirely ridiculous.