Dice stacks are a stack of dice of the same size with a name that describes them. Dice are either stacked in your favor, which means you can roll them to improve your rolls or defenses, or they are stacked against you, which means other people can use them to improve their rolls against you. Just like with skills and backgrounds, the name of the stack is how you determine if it makes sense that you can take some dice from it.
How do you stack dice?
Whenever you try to create an advantage or disadvantage for yourself or someone else, you can test an attribute to Help or Hinder them. You might duck behind cover to be 2d8 Protected by Barricade, read up on a monster you're hunting to gain 4d6 Knowledge of Cockatrice Weaknesses, or appeal to the room with a suave remark to get 3d10 Favor of the Crowd. You can also stack dice by using special abilities or items that say they stack dice for or against people.
What size of dice are stacked depends on the quality of the advantage or disadvantage created. Hiding behind a rotting fence might only give you d4s, while positioning yourself behind concrete might give you d12s. Ultimately, this is a gamemaster call so if you're thinking about stacking dice, feel free to ask them what size of dice you'd be stacking before you try to do it.
Your GM will likely stack dice when it makes sense; automatically stacking dice for somebody when they start an action scene with the upper hand, or against somebody when they wade into a sucking bog.
How do you use stacks?
When you take dice off of a stack, you can either roll them to improve your roll for a test, or you can roll them to increase the difficulty of a test for somebody else. There's no limit to the number of dice that you can take from these stacks, as long as it makes sense that the stack would help you out on your test or make the other person's test more difficult.
How long do stacks last?
When the last die is taken from a stack, the stack is gone. If you had dice stacked against you, you have either recovered from the disadvantageous situation or figured out how to deal with it. If you had dice stacked in your favor, your tactical advantage might be no longer applicable or might simply no longer provide the benefits it once did.
Your GM may also clear stacks whenever they no longer make sense. Being pinned down by covering fire only makes sense for as long as there's somebody out there actively raining down bullets on you-- if they get taken out or have to focus their attention elsewhere, that stack should go away. Stacks also probably shouldn't last longer than a session, but if it makes sense it's ok if they do.
How do I get rid of dice stacked against me?
Dice stacked against you can always be resisted. If you're 3d6 Tripped Up, you can test your Agility to regain your footing. If you're 1d12 Scared to Death you can test your Will to steel yourself. When you do whatever makes sense to resist the dice stacked against you, you can test an attribute to Help yourself, removing dice.
Examples of stacks
2d6 Inspirational Bravery is stacked in favor of the inspired and can be used whenever they could benefit from steeling their will.
4d10 Seeing Shadows is stacked against the afflicted and could be used by anyone who wants to use a character's hallucinations against them.
3d12 Cover behind the Parapets is stacked in favor of anyone behind the stone fortifications and could be used to protect yourself from arrows and other dangers.
6d4 Waist Deep in Sewage is stacked against the hapless wader, and could be used by monsters lurking under the water or a sniper taking advantage of the character's slowed movements.