Recycling: If the furniture is predominantly metal or rigid plastic, set it out next to your recycling container on your recycling collection day.
Garbage: If the furniture is predominantly wood or fabric, place it out with trash. Wrap mattresses in plastic and place on the curb with regular trash.
Visit the NYC Stuff Exchange to find a place to sell or donate used furniture in good condition. The green truck icon indicates that they may pick up goods from your home.