In the event of nuclear fallout, the first thing to do is stay calm. While this would certainly be unprecedented, it’s far from impossible to survive such an event. A quick word of note: This is addressing a situation in which nukes have either been launched, or the fallout has already set in.
Detecting the threat:
Sensors report that hundreds of nukes across the world have been launched (either due to a geosocial event that likely wasn’t broadcast to the public, or by pressing the large button in the command room).
The radiation counters in the control room report that the world has been irradiated.
You step outside and wind yourself standing in a nuclear wasteland that you're certain wasn't there when you parked your car this morning.
Analyze the threat:
Are the nukes still in the air? If so, take shelter and wait until you can begin analysis at point 2.
How close did the closest bomb hit?
Is the radiation survivable?
Have creatures began to mutate?
If so, how much? Consider exposing yourself to radiation in the hopes of gaining mutations as well.
Has anyone started organizing raider groups?
Combat the threat:
In this type of apocalypse, short of massive radiation scrubbers that could cleanse the planet (technology that we have yet to achieve. If the Hail Mary button was used to instigate this apocalypse and the aliens managed to survive, consider asking them for the technology to clean the planet back up), all that can be done is to thrive and reconstruct the old world.
Found a new government. People look to strong leaders in times of crisis. Be that leader. Though be ready to turn over control once the United States government manages to send envoys your way.
Establish a system of communication across long distances. Carrier pigeons should work excellently for this, especially if they’ve developed any good mutations to help them fly farther. This may be less effective if they develop mutations that throw off their homing abilities.
Establish a new economy. Money will likely be considered useless, so find a new currency to use. This can be done by minting your own new money (though this will likely be quite easy to counterfeit), or finding some sort of old-world material that could function as a proper currency.
Purge the world of threats. In the post-nuclear world, there will likely be plenty of issues to fight against, including mutants, wild tribal rituals, and aliens. Do your best to ensure that these threats are extinguished as quickly as possible to ensure the rapid rise of civilization once more.