I’m going to say this right now; in the event of nuclear warfare, those of us currently living in Newcastle are probably going to get vapourised by a bomb. However, this would make a very short article, so let’s assume Sunderland gets bombed instead.
The first thing to do with a nuclear apocalypse is to run the taps with the plugholes closed. This should provide a suitable amount of drinking water before the utilities are shut off; bottle up what you can using glasses or bowls, and cover with clingfilm. While those taps are running, make sure that all your curtains are closed; if there was a window open in that room, do not go in, just close the door and make sure you never go in there again.
The second thing to do is sort out your food supplies. You’ll want to survive at least two weeks before even thinking of venturing outside. Prioritise eating things in the fridge or freezer, as these will go off sooner. Uncooked meat is effectively worthless, as cooking it on an open fire in your home is several layers of stupid; uncooked eggs are perfectly fine, as salmonella occurs in only 0.012% of eggs.
In terms of radiation dosage, exposure will reduce itself over time, and distance will also limit your exposure. If you figure out your distance from the nearest nuclear blast, and the time since that blast, you can figure out how long you can stay outside for.
Radiation exposure (mGy/h) = 4000/[time^1.18 (h) × distance^2 (km)]
If the value is above 10,000, going outside will kill you in an hour, as 10,000mGy of radiation is enough to kill anyone. For comparison, 20mGy is the recommended maximum of radiation to receive over the course of one year.
When venturing outside, breathing in nuclear fallout or getting it in your eyes can be deadly. If you don’t have military rebreather masks, you can make do by wrapping paper towels around your nose and mouth, and wearing eye protection. Dispose of your contaminated clothes (and paper towels) afterwards.
Finally, I suppose I should mention treating radiation sickness. People with acute radiation sickness will have vomiting and diarrhoea after exposure. If it takes four weeks for symptoms to appear, then give them water and potassium iodide, and they should survive.
If they have haemorrhaging, hair loss, rashes and fevers, then they will likely die after a month. All you can do is make them comfortable – or take them to a specialist.