As others have said, it depends on the scale your talking about.
Your issues are mainly going to be EMP, fallout, and other survivors.
In a full-scale attack, one of the first weapons detonated would be a high altitude burst. This is to disable all unshielded electrical equipment.
Batteries would cease to function, cars would not start, computers would be fried, etc. This is why military equipment is hardened for EMP, and
you’ll notice things such as fighters cockpit canopies are lined with a thin mesh of gold. Anything that can reach a grounding point, or is not
protected in a Faraday cage is going to be toast.
Next comes the actual attack. They will first hit any military installations basing missiles and bombers plus any command structure that can launch a
retaliation. This is the attack that will, long term, pretty much end life on the planet permanently. Since most of our launch sites are hardened
against such an attack, they use what is called a “Slow walk”. Here is a picture of what a slow walk looks like:
www.ki4u.com...
When a missile impacts a buried hardened structure it throws lots of debris in the air. This cloud of dust then protects the remaining missile silos
from incoming attacks because the dust cloud will actually destroy the fast moving incoming warheads, while at the same time still allowing the slow
moving outbound missiles to launch. So they dig them up, by hitting one, moving to another, waiting for the dust to settle on the first one, then
hitting it again. This will throw so much fallout into the upper atmosphere, and the jet stream, that it wall literally coat the planet in this
radioactive ash.
That ash is going to be in the water, the air, coating every surface on the planet. Once you inhale or ingest enough of it, you will slowly and
painfully die from radiation poisoning. Then as an added bonus, this ash will create a layer in the upper atmosphere, cutting off sunlight, and
causing a nuclear winter. Pretty much any life that is left on the surface, that has not died of radiation poisoning up to this point, will slowly
starve to death before all that ash dissipates.
Of course they still will hit all the production and population centers just to put the icing on the cake.
If you can manage to survive the fallout ash long enough for it to decrease in radioactive strength (bunker down somewhere), you might be able to move
around outside, that is as long as you don’t kick any up and inhale it. All the surviving wildlife though will have been exposed to it, and if you
eat their meat, you’ll ingest the radiation yourself. Of course it will be in all the water sources too, and if not properly filtered, again
you’ll ingest it. It might take years for all that ash to wash away to acceptable levels without humans cleaning the area up. Of course until all
the ash is out of the atmosphere, every gust of wind or drop of rain will bring fresh fallout to the area.
As to people, well... You just played fallout, so you kind of don’t need me to explain that…
There’s a reason it called Mutually Assured Destruction (MAD).