In the kitchen/bathroom: Give your child a spray bottle filled with water. You can add a drop of vinegar, essential oil, or bleach to give it that "cleaner" smell. Now give them a rag and tell them to "have at it". They LOVE to spray down cabinets, floors, walls, doors, baseboards, appliances . . . You name it.
In the living room: If your child is five or older, allow them to vacuum (with supervision, of course). Smaller children can "dust" (make sure any sacred breakables are put up and out of reach, first) with an old rag. Older children can dust knick-knacks.
This is what will happen - either 1) Your child will get REALLY into helping, so you gain an assistant or 2) Your child will botch at having to help (this is usually the older ones) and go retreat to their rooms. Either way, you get what you want!