STEP-BY-STEP
Assign everyone tasks they can reasonably do on their own. Our 4 year old can clean the bathrub (well enough, she's proud and so am I!) Our 9 year old vacuums, 6 year old loads the dishwasher, etc.
Everyone wants to see the fruits of their labor. Take a before picture, set a timer, and get cleaning!
When you're speed cleaning, you should take frequent breaks. This makes your kids more likely to help out next time. For a job well done, offer rewards, like ice cream or slushies at the end of your project!