1. Get children drinks (or, even better let them get their own) whenever requested. Water is best, but anything works.
2. Allow children to use various different cups for each subsequent drink throughout the day, as they instinctively are unable to reuse cups.
3. Normal children in the wild (my house) will naturally leave these cups just about wherever, so I suppose yours will too.
4. Normal children in the wild will commence spilling said drinks at the rate of 2.7 per day.
5. Simply and quickly mop up all spilled drinks.
Within a week, this method guarantees that every inch of your tile and/or hardwood floors will be spotless and shiny, and, as long as you continue this method, will remain so eternally.
PS: Not recommended for carpet. Carpeted households should only allow children to drink outside. Water bowl optional.