Mix in a shovel full of regular soil.
Add dry raked leaves (I never rake in the fall)
Add kitchen scraps, even the acidic stuff like citrus and onions.
Add plant material from dead headed flowers, cut grass etc. But no pernicious weeds.
Stir every few days with a fork.

My compost is just a pile on the ground. I keep an eye on the moisture content and keep adding stuff every week all season long. It will work quickly and when you need compost you can either sift it, or use as a top dressing, and put the bigger chunks back in the pile. Also chop up food scraps into smaller pieces, or toss the larger pieces to the side of the compost to work in later.

I did two types of piles as an experiment. One had all the ingredients layered but it was never turned. The other was turned frequently and became good compost much faster. Last year I did not have to add water at all because we had ample rain. An old carpet can always be placed on the top to prevent moisture loss, and retain heat.

I read also you can cut Comfrey and add it to compost. Supposedly something in it acts as an “activator.” I will be testing that this year. Your chickens will like Comfrey anyway.