Show off how clean you are and what you do as cleaning. Whenever they make a mess, call them so they can clean it. If they refuse, keep the mess there until they clean it.
I have roomates, and none of them like cleaning, and when asked to clean, will always pick the smallest, least dirty area that they can find. This leaves larger areas like the kitchen and living room a disaster zone. One good way I've found to balance the cleanliness is through competitive gaming. Racing games work very well, but try to chose a game that everyone has equal footing in. Everyone comes together and plays the game. The winner gets to clean the smallest area, the one who comes in 2nd gets a bit bigger one, and so on. The last place person has to clean the biggest area. Now, we're all grown, and a tactic like this might not work for a family with younger children. Younger ones might need to be motivated by promising to make their favorite meal for dinner, or not being able to play their games or watch TV until their assigned areas are tidy.