If possible move upwind, as far away from any military or industrial targets as possible. Otherwise, shelter underground or in a concrete/stone building. Put on the best dust/gas mask you can find. Put on heavy or waterproof clothing and try and cover as much skin as possible.
I work in nuclear security so this is kinda my thing. If you're in the fireball zone you're pretty much toast, other than that it's mostly about avoiding the blast pressure wave (as well as secondary effects like buildings collapsing on you) and exposure to airborne fallout, which is most dangerous in the first 24-48 hours. After that it becomes much safer to move around.
Sure. Nuclear security is a broad area and it can mean a whole lot of things, but mostly it means more to do with non-proliferation and defense against and response to nuclear threats on a technical level and less the mechanics of training people what to do in the event of a detonation. It'd usually fall into the spectrum of nuclear engineering, though it can be pretty multi-disciplinary (e.g., my educational background is in nuclear engineering, applied math and CS).
In my case I'm in research; specifically I develop algorithms for locating radioactive sources using sensor networks distributed through a city. My educational background focused heavily on non-proliferation and nuclear forensics. One of the things we studied in my graduate career was how to optimally sample fallout in the immediate aftermath of a detonation based on predicted dispersal in order to get the best quality samples (for forensics work) while minimizing the risk to first responders. Spent a decent chunk of time learning about all the sorts of dangers you expect from a nuclear detonation.
I would've called my parents and then try to find cover. As pessimistic as I am sometimes, there's just enough paranoia on this issue to make me take it seriously.
I would seek shelter in a subway station. It’s not perfect in terms of protection, because the ventilation system would pump in radioactivity as long as there’s still power. But it would allow me to get to any place 20km away from city center without going above ground once.
