After our really rainy winter, which we did not cover it, it got way to wet and stopped cooking. But now its working really well.
Ideally, your compost should be 2 parts mature material (carbon, woody, slower to decompose stuff), 2 parts immature material (green, quick to decommpose stuff), and 1 part dirt, water and oxygen. If you had space in you garden, you would make a few piles, consisting of multiple layers of these materials, and let it sit for 3 to 4 months, being sure to keep it evenly moist and then it would be ready. No turning required.
Our compost is made up of a combination of kitchen scraps, weeds, clippings, prunings, straw, and chicken manuer. Every time I double dig a raised bed, I remove a row of soil (to make room for adding fresh compost), and keep that in a pile near the compost, so it can slowly be added when needed. Usually we might put a shovel full on the top, to cover all the green kitchen scraps, trying to keep to the formula. As home gardeners, we only have room for one pile, and we add to it daily. We turn it to give it oxygen and water it frequently in the summer. Most items decompose fairly quickly within 4 - 6 weeks.
This winter I am planning to focus on cover or carbon crops, so I can work towards keeping my home mini-farm sustainable, not having to depend on outside sources of compost, keeping a closed system, which is healthier for the whole environment, not just my backyard. Goods winter cover crops in my area are cereal rye, fava beans, oats, wheat, one variety in particular I am intereted in trying because of its unusual beauty is Black Emmer.
Good summer carbon crops would be comfrey, corn, sunflowers, amaranth, quinoia, sorgum or broom corn. One I am particularly interested in trying is Amaranth. It is what you call a "catch" crop. In the middle/end of summer, when your summer crops are done, and it too late to plant a new summer crop, but too early for fall crops, you can plant amaranth for your compost. It grows very quickly.