My parents don't really get my siblings to clean much but I think it's important for them to learn how to do basic chores, this is where my psychology classes come in.
My brothers can get really lazy sometimes, but I want them to help out sometimes, which is why I get them to help me wash my car. Most times it's actually them that's washing it and I just sit back and supervise. They like it because it's a car, and all boys love cars, and they get to sit on it, scrub away, use the hose and have a good time. If you want to teach kids about cleaning, get them to help wash the car, even at a car wash, and they will soon begin to enjoy themselves.
Pocket money is another good way to get the kids to start cleaning. I give my sister 50 cents to vacuum and dust my room every two weeks. It is only a small amount but I do only have a small room. She likes to vacuum surprisingly and it has become her responsibility, my mother doesn't vacuum her room anymore, she does it herself. Sometimes she can't be bothered but she does it eventually, it has to be done by the Sunday night otherwise she still has to do it the next day, but she won't get the money for it.
Making cleaning fun always helps, especially with younger kids. I like to make games of it like, 'whoever can pack away their toy box the fastest will get a chocolate', and then the kid who doesn't get the chocolate needs to work extra hard at the next task.
Give each kid a task to do around the house and put a timer on it. For example, "Chloe, you need to pack away all the dolls, the doll house and the dolls clothes, Ryan you need to put away the DVDs and the racing car set and put them in their right box, Cameron you need to clear away the plates from the table and the cups and then wipe down the table. Everyone has ten minutes, go!". This is what I do sometimes when I'm babysitting, and the kids rush off and pack away their designated toys and then come back beaming that they did it before the timer goes off. I don't usually give them a reward for it, but they do like the game.
Those are some easy ways to get kids to clean up. Even if its just teaching them to clean up their room and packing away their toys and mess, before they start doing chores like vacuuming and dusting.