There are a variety of tips for quickly softening hardened brown sugar here: 10 Ways to Soften Hard Brown Sugar .
The one that worked best for me personally, when I had to do this in a hurry, was to chip off a large chunk of the hardened sugar, put it in a (microwave-safe) Ziploc bag with a damp paper towel, and microwave it for 5-10 seconds at a time until it was soft enough to use.
Don't pierce the bag; the whole point is to allow the steam to re-hydrate the sugar.
But obviously don't leave it in the microwave for too long either,
otherwise the bag will either melt from the heat or explode from the steam.
You should also let it cool for a minute or two between zaps; the sugar will continue to absorb moisture as long as the steam can't escape.
I also use the paper towel trick if I need to re-hydrate the sugar the day before.
Place a piece of wax paper on top of the sugar, then a damp paper towel on top, and seal it.
It'll be good as new the next day.
Don't leave the paper towel in there for too long though, otherwise it'll grow mold (doesn't seem like it should, but I personally witnessed it happen).
I like this method because it doesn't require me to waste any apples or bread, if I even have any around.
cooking.stackexchange.com/users/41/Aaronut
When I have hardened sugars, especially when I first buy rocks of jaggery, I'll grate it like a hard cheese, which turns it back into a powder very quickly.
cooking.stackexchange.com/users/1236/stephennmcdonald
Easy, place in food processor and process until powdered One damp it will clump together again if stored, so
just process what you need Adding steam or heating
it will more than likely make it unsuitable for storage
cooking.stackexchange.com/users/3203/TFD
Wet a dishtowel.
Make sure that it is really wet almost dripping.
Microwave it for 2min.
Be carefull it is really hot and steaming.
cover top of bowl( Do not touch brown sugar)Microwave another 30 sec.
Let set for 1 to 2 min.
take out.
Break up with for and hands.
cooking.stackexchange.com/users/17787/Cyndi
I know its not quick, but I store a slice of bread with my brown sugar.
Softens up hard sugar and never let's it get hard if a new bag.
cooking.stackexchange.com/users/18769/Rachel
I've done this before by steaming it.
I used a large pot of water and suspended a bowl full of brown sugar above it.
After a few minutes, it was soft enough to work with.
It seems to me the same can be done with a tablespoon of water in a bown of brown sugar in the microwave.
Just cover with plastic wrap and pierce for a couple steam vents.
Just don't cook too long or the sugar may start melting.
cooking.stackexchange.com/users/3234/FoodTasted
Put it in a container in the microwave with a small bowl of water beside it.
Microwave for 1 minute; check and (if necessary) microwave for another minute--
making sure you don't overdo it.
It worked GREAT.
cooking.stackexchange.com/users/11073/Karen
Who says you need to buy a cute terra cotta teddy
bear?I left a small terra cotta planter outside during winter and rescued 3 broken pieces that weren't sharp.
I washed them off, dried them, re-wet them with hot water and stuck them on top of the brown sugar.
I closed up the bag and within 15 minutes, the top of the sugar was soft ~ 1 cup worth.
I repeated the process and it softened further.
cooking.stackexchange.com/users/18110/Roberta
Years ago I use to siice an apple in half....
place it on wax paper and place the paper on top of the dried brown sugar.
It use to work.....
haven't had to do it for years.
Hope this works for you.
cooking.stackexchange.com/users/27007/Treva
I found the fastest and easiest way to accomplish softening brown sugar was to place the brown sugar on to a paper plate, then place an additional paper plate over the top of the brown sugar.
I then used the top paper plate to smash down the brown sugar.
Then I took my hammer to it and smashed it, it was nice and fine and soft after wards.
Then you just dump it back into your container.
Takes less that one minute to soften brown sugar.
cooking.stackexchange.com/users/34812/laurie
Place the brown sugar, in an extra large airtight container.
Boil water, and put into a cup
(I usually use a couple of ounces).
Put the cup into the container, making sure that the cup and water does not touch the brown sugar, close container and leave for 30 minutes or until soft.
Remove cup carefully, making sure not to spill water.
My smart sister would place open bag of hardened brown sugar in a large airtight baggie.
Add a slice of apple between the brown sugar bag and the baggie so the brown sugar wouldn't come into direct contact with the apple.
Close airtight baggie, when brown sugar is soft, remove apple.
cooking.stackexchange.com/users/21992/Kyera
Place the sugar in a ziplock bag and pound into powder with a rubber mallot.
cooking.stackexchange.com/users/17471/Issac Spicer
boil a pot of water, take the pot off the stove and sit the brown sugar container in it...will soften up beautifully in about 10 minutes or less.
Easy/Peasy
cooking.stackexchange.com/users/53853/Jade Dragonm
All of these are fine methods.
Over the years, since I don’t use brown sugar so often, I just use granulated sugar and add some molasses to it.
then I never have to worry about my bag ofbrown sugar turning into masonry.
Its a nice experiment to add molasses to sugar and mix it and see it magically become brown sugar.
This will also help you determine how much molasses to add in the future (in nearly all cases you do not need to actually combine the sugar and molasses, but you can just throw both in at the same time.)
cooking.stackexchange.com/users/76107/John Meyers
I had some brown sugar that didn't get properly sealed and so now it's too dry and solid as a rock.  What's the quickest way to soften it up and get rid of the clumps? Folks have suggested leaving an apple with it in a bag overnight; any suggestions of a shortcut for rehydrating that takes minutes instead of hours or days?
How to quickly soften hard, dried out brown sugar
cooking.stackexchange.com
<sugar><brown-sugar><moisture>
cooking.stackexchange.com/questions/8902
cooking.stackexchange.com/users/198/notpeter
You can steam chunks or microwave them with a damp paper towel for a few seconds at a time until soft. Other options include grating it like hard cheese or putting it in a ziplock bag and pounding it with a rubber mallet. There are lots of easy methods: microwave or steam, grate it or use a rubber mallot to break it apart.
Chip off a large chunk and microwave it. Try grating it. Put it in a steamer. Use a rubber mallot to break it apart.