There are plenty of books around with which civilisation can recover. Even if 90% of the population died, that would only take us back to population levels of the 1700s. A 99% death rate would still leave 650k people in the UK and over 10M in India.
Unlike the 1700s, how many people today know how to farm, fish or hunt? To weave? To construct a house?
However we don’t have to invent those technologies. We already know farming and weaving etc exist, so we just have to start learning and trying to figure them out. We humans are great innovators and learners, so assuming we have enough supplies to live on short term, people can adapt.
I think we have to know how long this blockage would last. And what is our real goal here? Maintain current population levels and American standard of living? No way. Can’t be done. Petroleum availability alone would be devastated when the sea temperatures dropped.
Just two hundred years ago, the human population endured a “Year without a summer” and it’s hardly even spoken of today. Obviously one year is survivable.
As for nuclear power, I’m not sure that’s really necessary. Moving homes under the earth will protect us from the severe cold, and a good windmill will provide enough energy to keep LED grow lights going. (Check the aquarium stores, there are quite a few around.) There are quite a few “Preppers” out there who are ready for up to five years underground.
I’m not sure what’s left of society would be one I’d like to live in though.
What do we do with all the dead bodies? Mass cremations(wasting valuable fuel)? Soylent Green 'em(would we consume it)? Drop them at sea? Just thinking about all this gives me the heeby-jeebies. I guess I better squirrel away a cyanide capsule. 
Well, the sun is a source of energy. If it got snuffed out we would need another source.
The most likely candidate would be to burrow underground and use the earth’s heat as a source of energy. Surprisingly you do not need to go all that far down (relatively speaking) before it starts getting uncomfortably warm. We already need to provide massive cooling systems to keep mines in a tolerable temperature range for people. It gets surprisingly hot surprisingly fast as you dig down.
So we can cover not freezing to death easily enough. Not for the current population but enough people to not lose the human race.
The next parts we need are food. So we need to generate energy to power lights to grow plants. We could do it with nuclear power or, perhaps, geothermal power. We do it now so nothing new needed there.
Last I am not sure what we could do about. Without plants producing oxygen I assume that over time the earth’s atmosphere would become unbreathable. I have no idea how how long that would take. The atmosphere is huge and most humans and animals would die so not sure how that works out in the end. With energy though we could extract oxygen from water and of course the plants we were growing would help a bit.
In the end the human population would mostly die but it is conceivable some few thousand or more could survive.
As long as books from which we can learn these things survive, this won’t be an issue.
Going back to the premise of the OP, its unlikely that libraries will survive. Or, if they survive people will be able to find those that do. Especially in looted and burned out cities.
I wonder also if a 21st century library would have how-to books on such antiquated subjects. They likely would have been dumped to make room for DVDs and computers. 
There are thousands of public libraries in the UK alone. And then there are all the books in private houses.
But the knowledge will be there anyway in many if not almost all farming communities, which will survive when cities will fall.
There is a huge difference between inventing something for the first time and figuring out how to do what you already know exists. Might not be weaving medieval tapestries, but people will figure it out something usable.
I’m not sure the lost-knowledge aspect of this is all that much of a concern. With just a few hours of time, someone could Google and save all sorts of information on farming, construction, and other topics on a basic laptop.
Under the premise of the OP, the internet would be down.
If the sun goes away suddenly, would we have enough time to dig in/down and survive? What would the cooling off period be like?
Who needs grow lights ? Shrooms, baby, shrooms. They’re already grown in caves and mineshafts. Most species like it dank and dark.
Hope you like fried portobellos, 'cause that’s all we’re eating from here on out.
The OP started out with “Assume a supervolcano or meteor blocks out the sun for an extended period of time.”
If it’s a meteor, I assume we’d get enough advance notice that many people would be aware of it hours or days before impact. Sort of like hurricane warnings today. As for the supervolcano … if one erupted on the other side of the planet, I’m assuming it would take hours / days to spread particles throughout the entire atmosphere.
So, we ought to have at least a window of a few hours, and even without sunlight, there’s no reason that ISPs and power has to go out immediately. It could keep running for days / weeks even.
This is an excellent question. Air temperature drops pretty quickly without the sun (like 10-20 degrees overnight), but I assume that if it were to continue dropping that that would be counter-balanced / slowed by heat radiating from reservoirs like the ground / bodies of water sooner or later. Would that be before we all freeze to death? I don’t know.
Would it be possible to get an estimate of the temperature at one week, two weeks, and maybe one month…then an estimate of how long it would take us to find a way to survive during that period of time, if it is possible at all?
This video guy says that the average surface temperature right now is 14 degrees Celsius, and that after one week without the sun it’d be down to freezing (0 degrees). After one year, he says the average temperature would be -73 degrees. So … you’ve got maybe a few weeks or months for some very frantic, very cold, excavation work. Probably better off spending that time searching for a pre-existing cave / mineshaft to move into.
He says the best bet would be to move to geothermal areas like Iceland or Yellowstone. Also, the ocean depths would stay liquid for billions of years, even though the surface would freeze over within a few years or less, so if you could find some way to sustain life deep in the ocean, you’d be alright. We manage to keep small numbers of people alive in space and submarines for months at a time. Do we have technology to split oxygen out from water, while underwater, and make breathable air out of it?
Yes. All that takes is electricity. Nuclear subs generate oxygen this way.
Not sure about this, yes there would be some underground hoarding, but humanity is full of those bastards who hold on to the reins of power through force, slavery, fear and punishment. The motivation of the end of humanity is enough to motivate mindless loyal people to serve to the point of death.