Just wood shavings, chicken poop and some moisture will compost. You don't need anything else. It's more about the amounts of each, just like in a compost pile. Some people use other litter choices, I normally use wood shavings.
If you read anything about composting, it will help explain about the process. In a coop's litter, the chicken poop is like the green, wet, high nitrogen ingredients of a compost pile. The wood shavings are the brown, dry, carbon ingredients of a compost pile.
Compost piles in the garden can be manipulated to run very hot, with a lot of microbial activity that creates heat. They can also be run cooler, with less microbial activity.
For a garden compost pile, a hot pile is great. It kills pathogens in the compost, like plant diseases or bad bacterias, kills weed seeds and is done really fast. The optimum ratio of ingredients and stirring or turning the pile help create a hot pile.
A cool pile doesn't have the same purifying effect and takes longer. However, you still end up with great compost and it's less work. It doesn't require all the turning, which is done to redistribute the microbes, redistribute the ingredients the microbes are using for food and provide oxygen for them. It's more of a set it and forget it method.
In a coop, a slow, cool process can be good. You can let it finish off in a pile in the garden for a bit, after you clear out the coop. A little more activity can add warmth to coop in the winter. I don't think you'd want to run a coop litter as hot as you would a garden compost pile, as chickens are living on it.
Litter or compost that's stinky has too much moisture and needs more of the dry/brown/carbon/shavings. Smelling ammonia in the coop is also a sign of this, in a well built coop that has the normal amount of ventilation.
Litter or compost that's dry, cold and inactive needs more wet/green/nitrogen/chicken poop to become more active. Dusty litter is traditionally caused by litter that's too dry. At this point in time, it can also be due to people that have added dust to their litter, especially in excessive amounts.
As chickens poop in the coop over time, you need to add more shavings over time. Starting with enough shavings to cover the floor, you can add a bit more as needed on top. You often only have to add it in the areas where the chickens are pooping more. the chickens will do a lot of the stirring and moving of shavings for you.
Some people start out with a very deep layer of shavings and regularly stir the shavings around to redistribute everything. I don't like the extra work with that method. I prefer to have the litter and chicken poop layered as the litter builds, combining as they go. Once the litter is deep, it's not like you're going to want to dig down a foot or more on a regular basis, anyway. So, you may as well start out layering it in shallow layers.
If you crowd your chickens, you'll end up with a certain amount of poop crusting and need to break it up and stir it in. I don't like having to do that. I usually don't go less than 5 square feet per chicken, so that hasn't been a problem for me. I once read that at 4, you only get a little crusting/clumping that needs to be stirred in and at 3 you get more.
For a large walk-in coop, I don't crowd, keep a bale of shavings in the corner with a scoop and occasionally fling a couple of scoops on top of the litter where needed. I like to scoop it all out in the spring. If you find that the litter is wet and repulsively stinky in the bottom layers, adjust your management. It was too wet down there. Add a little more shavings during the year, as the litter is building.
I see some people that have a lot of shavings, very little chicken poop and almost no moisture in the litter. That's not going to compost. Which is fine in the short term, but if you leave it a long time the poop can break down into dry dust. Then when it's dusty and gets stirred up by movement, you and the chickens are breathing feces.