A really super quick and easy compost bin that we're using here in suburbia....
Get yourself four pallets (same dimension, if at all possible). Using about 8 to 9 old hangers (the thick wire part), straighten to form wire again (not a hanger), use that to 'tie' the pallets together to form a standing square. Leave 'front' openable, using one hanger on edge that will be the 'hinge'. Can close it to keep chickens out of pile - relatively speaking. If you'd like, you can also put one on the 'top' but that means getting the stuff in and/or out is trickier. Not impossible, but my kids don't have very good 'aim' yet.
Compostable materials include all vegetable matter, fruits, rinds, skins - but no dairy or meat products. So if you've got butter on that sweet potato - well, cut it up finely and feed it to your chickens, not to your compost! I also squish my empty eggshells pretty finely (just with the back of a spoon in the compost bucket which lives near our sink), so I don't encourage egg-eaters.
Compost works really well to fill in divets and bumps in your yard. Simply sprinkle a fine layer over the grass using a shovel and a wheelbarrow (rake if you've got bigger pockets). It feeds your lawn very nicely - but bewarned, you'll need to mow more often - which means more green stuff for your compost bin or your chickens!
Hope this helps.