In accordance with environment legislation: asbestos or fibro, tyres, food, liquids, gas bottles, flammable containers and general hazardous materials including solvents, paints, acids, oils, poisons, needles & syringes, explosives and any other environmentally unfriendly substances or objects likely to cause harm or damage. To dispose of these materials you need to contact your local council.
Most all other wastes such as greenery can be mixed with household and construction/demolition wastes.
There is no exact way of telling if you have asbestos, but as a general rule houses pre 1980 are likely to contain some in the fibro cement sheeting found in the bathroom and eaves of the house.