it's pretty traditional to empty your coop out onto your garden after the harvest and let it decompose over winter. Exactly when you do that will depend on your climate.
I have a droppings board and use the pure manure in my compost, along with the debris from the garden and grass trimmings. I may get two batches of compost a year, but I don't work it that hard. I'll probably only turn it once.
I mulch a lot of things, usually spreading a layer of newspaper and covering that with straw, dried grass trimmings, or year old wood chips and turn all that under when it's finished. That stuff decomposes and really adds tilth to the garden, plus keeps weeds down. It's a whole lot easier to get the garden ready for the next year where it has been mulched because the weeds and especially grass has not taken hold. I don't plow mine under but turn it with a spade or by using a mattock to mix it up. The wood chips need to be a year old or they won't decompose enough to just turn under. I age mine in landscaping beds.
If you have cows or horses, you can spread manure in the fall, just like cleaning out your chicken coop, but that tends to spread a lot of weed and grass seeds. If you can compost that stuff and get it to heat up you can kill a lot of weed seeds, but animal manure is a great fertilizer. Except for rabbit manure, it is all too hot to put directly on growing plants so it needs to break down first.
