Organic matter for compost comes in two general forms: fresh, green material and brown, woody matter.
Fresh, green material is high in nitrogen and includes kitchen vegetable waste, coffee grounds, fresh weeds (before they go to seed) and herbicide / pesticide-free grass clippings.
Brown, woody matter is high in carbon and is found in fallen leaves, straw (not hay that has seeds), uncoated newspaper, corrugated cardboard, wood chips, sawdust and similar matter. Dried horse, cow, poultry and pig manure are also sources high in nitrogen and can be added to compost. Manure that is not yet dry, but is still 'hot', cannot be added directly to plants, it will damage them.
Compost your weeds, too
All the discarded leafy materials, including weeds (as long as their flowers have not yet produced seeds) from your garden can be added to your compost pile.