To make good compost you need to have the right mix of carbon and nitrogen (Browns and Greens). If you have too much nitrogen your compost will be a smelly sludge heap, too much carbon and things will not compost.
This is a list of compostable materials:
Greens (High in nitrogen): grass clippings, kitchen scraps
Browns (High in carbon): Leaves, woody materials (not all woody things can or should be
The Big PileWe have horses so we have an (almost) unlimited supply of manure. Because we have so much compostable material all the poop gets put in a big pile. Horse manure is the perfect mix of carbon and nitrogen. We don't use shavings but if you do your pile will have too much carbon.
Our pile provides us with as much compost as we can use. (A lot more, actually!)
Pros: It doesn't require any work other than putting in poop and hauling compost out.
Cons: Doesn't work unless you have horses.
Put the chickens to work!
I have chickens so all the kitchen scraps and old hay go to them. They eat what they want and leave what they don't want. The leftovers gets scratched up and turned into compost. The hay keeps the weeds down in the unused part of the garden while it's getting composted .
Take look at Harvey Ussery's book The Small Scale Poultry Flock for more ideas on how to put your chickens to work.
Pros: It's fast and the chickens do the work.
What they eat they poop out and add to the compost.
If you have them do it in the garden you don't need to haul the compost to the garden.
Cons: Doesn't work unless you have chickens.
This method may work with other poultry but I haven't tried it.
I have heard of this in the book All New Square Foot Gardening by Mel Bartholomew (but I have never tried it). You put the ingredients in a barrel and put the top on. Then you roll the barrel around every day and ta-da! Compost!