Streamline the organisation of your house if you want your children to be able to help with housework. Keep the brooms, mops and dusters in one place. A three-year-old can use a pan and small brush.
Keep handy a portable carry-box with household cleaning supplies. Mr Sheen furniture polish, wipes, Dettox handiwipes and Swiffers are useful. (Floor cleaning liquids, Jeyes fluid and so on are important, but your children must be past the stage of drinking the stuff if they're to have access.)
In the kitchen, keep paper towels and a bottle of spray cleaner at the ready. In the bathroom, have some cleaning spray and a sponge-cloth handy for them to clean up the sink. Keep the vacuum cleaner within easy reach.
Keep delicate, breakable things out of the way. Don't expect children to clean around them - that's impossible.
Plates and cups that children use regularly should be plastic and on a shelf within their reach. If you want your child to clear the table and load the dishwasher, then use sturdy, inexpensive, easily replaced dishes (Rayware have a good range). There's no point getting angry at children for breaking something if they're going to the trouble to help.
Enforce the golden rule: all eating at the table. (Fresh fruit might be an enticing exception, as long as children throw the cores and peels in the bin.) Once you allow any other kind of food consumption on the sofa or in the bedrooms, you're lost.
Keep eating in front of the TV (popcorn, pizza) as a special treat, possibly on a weekend night - a reward for keeping things tidy.
Teach children to clean up after themselves when they've made a sandwich or poured a drink. Do teach them to make a sandwich, by the way. Have the bread, a safe knife and their favourite fillings in a familiar spot. Keep the sponge or paper towels in a convenient place and show them where the bin is!