It will produce ammonia under the right conditions, which is why you need to make sure you have some airflow in the coop during all but the coldest nights, so it doesn't build up to dangerous levels.
It's like any fertilizer, you can use it immediately IN THE PROPER AMOUNTS. Too much, and you'll fry things, though.
If you're using a litter in the coop/pen, such as shredded newspaper, straw, or leaves, the birds will do an excellent job on their own turning the litter on a regular basis and mixing the droppings into it. If its kept dry, it doesn't do much of anything, just sits there, waiting until it get moist enough to react (probably needs a certain moisture content to allow microbes to survive in it).
Moist litter will break down pretty quickly -- on average, I'd say its generally safe to spread and use in the garden in about 30 to 45 days after you begin composting it. That will depend upon the conditions -- warmer and wetter it is, faster it breaks down, just like any compost.
I use oak leaves for the most part as litter in my bird pens -- I find that they make a great litter - they last longer and stay "fluffy" compared to straw, even when they get wet. And, of course, they're free for the gathering in the autumn and again in early spring along the curbsides on trash day. If I don't have oak leaves, I use straw, but the oak leaves do a MUCH better job of keeping down odors in the warm months -- I think it must be the tannic acid in the oak leaves. The only down side I've found to oak leaves is that the tannins stain white feathers a brown over time, the same way that tea can stain a white table linen. But that comes out in the moult.
Something that is interesting in the winter is the fact that the waterfowl make their own "hotbed" because they are naturally more "moist" both in the droppings and in the amount of water they splash around the pen. The moisture level in the waterfowl pens is enough that the litter decomposes and creates a gentle heat. The "upland" birds I keep - chickens, turkeys, Japanese quail, and Chukars, don't have this effect -- their droppings are dry, the litter stays dry, and doesn't begin to heat up until I clean it out of the pens and compost it by adding moisture.
I use shredded paper in the nesting boxes, but I don't get enough of it to use as a general litter. I shred up my junk mail, etc. to get that, and I know that no one is going to piece that back together to get a credit card number after its been in the chicken boxes.
I use the "deep litter" method where I just keep adding new on top to keep it clean, until it gets too much, then I rake the entire thing out and start fresh -- I try to do that about once every 4 to 6 weeks during the warm months, and then it goes from mid-late November until about late March/early April without a cleanout because its just not practical in the winter.
When I clean it out, I do different things with it. Some of it goes immediately around large trees and shrubs, where the risk of burning them is minimal -- still being careful not to put TOO much on, of course, as anything can burn in excess. Some of it goes on vegetable and flower beds at the "off times" -- first thing in the spring, last thing in the fall, or during fallow periods in mid summer, so that it can sit for at least about a month before a new crop goes in.
Hope this helps. Enjoy poultry keeping.