If you want to sort out how to soften brown sugar, you should firstly know that when brown sugar loses its moisture, it becomes hard. So every technique used for making hardened brown sugar soft is aimed at returning moisture to the brown sugar.
Bread
This technique is ideal for you if you have enough foresight to know you will need brown sugar in a day or two. Keep your brown sugar sealed in a tightly sealed plastic container with one slice of a sandwich bread. The product will be a stale bread, which imparts the moisture on the brown sugar.
Apples
This is more or less like the first technique, but a good fall flavor will do it more good. Place your brown sugar alongside some slices of apple, after one or two days, the brown sugar will come out tasting great.
Microwave
Place your hardened brown sugar in a moderately large bowl and dampen with a paper towel. Microwave it for about 25 seconds. Don't let it stay longer to ensure the brown sugar does not melt to form a goo, this is the most effective method.
Marshmallow
Place some large marshmallows with the brown sugar. You can either use a bag or a sugar container, so long as it is airtight.
Damp Cloth
If you have adequate time at your disposal, place the sugar in a bowl and use a thick, wet cloth like a tea towel to keep it covered. Allow it to stand overnight. In the morning, it would have become soft again.
Store It the Proper Way First
Store it rightly can save you time wondering how to soften brown sugar. You only need two words here: Air-tight. Air and moist brown sugar are arch enemies, so storing it in a container that does not allow air passage is important. You have to keep the bag tightly rolled up, squeeze any air out, and use a rubber band to keep it wrapped. For more precautions, keep the original bag stored in a well-sealed plastic bag with a zip at the top.