I just emptied out my compost into my no dig garden bed so it's time to start again. I always have a few branches and sticks lying about so I start with them first. Layered over each other crisscross, the web of sticks ensures aeration at the bottom of the pile.
Some shredded cardboard is next and then a pile of freshly mowed leaves. Once doused with water I've then gone to the worm farm to get a scoop of dirt that will no doubt contain plenty of useful micro organisms. Every few days the kitchen scraps bin from the kitchen gets emptied into the compost. The kitchen scraps bin always has shredded newspaper mixed in with the kitchen scraps. I find it absorbs the moisture and doesn't get that vinegar smell as much.
Adding to the heap from here is a case of what becomes available but always being aware of having a balance of wood chips, sticks etc to fresh green waste. I have a lot of debris around the garden from trees so I'm often mowing up leaves and sticks at the same time. This mixed in with the lawn clippings always gets the ball rolling with the temperature of the heap. Ensuring the heap has a good moisture content is important too, and sometimes it will get a flush from the hose. Having a bin with a lid keeps the heat and moisture in but it does make it a little harder to turn, I usually stick in a fork and try to move it about, particularly trying to loosen up the centre.
I've got chickens so their manure always ends up in the bin. So do their egg shells and feathers for that matter. Any garden waste such as corn stalks, bean vines, broccoli stems all get thrown on the lawn to be mowed up and placed in the bin.
After a growing season or two has passed and I know I am going to empty the bin soon I stop placing new waste in the bin and I stockpile the waste, trying to hold off on adding more. I want to ensure that what is in the bin has had enough time to rot down. Then the bin gets emptied and I start again.