You can add just about any organic matter, vegetable peels, manure, eggshells, even used tissue paper and toilet roll/kitchen roll holders (carton). Here's a few tips:
Do not put grass cuttings in, it causes an anaerobic reaction (don't ask me what that means), DH is talking, I'm typing.
Onion skins don't break down well and are anti-fungal.
Ash keeps the acidity down in your heap.
Cow manure is the best for your heap.
Chicken poop is VERY acid, add lots of ash.
Earthworms will break it down a treat.
You can add soil/sand.
Add leaf mulch for fiber.
Turn the heap every few months, dig it over with a fork.
If you live in a dry area, water the heap now and then to keep it moist.
That's all we can think of now.
Enjoy!