On a day where there is a forecast of heavy rain, walk around your neighborhood.
Look for spots where the rain runs down a slight slope. The water should be less than an inch deep.
In the rain, or when the rain pauses, take your stones and lay out a course in that spot. Use the stones to make a curving path. Often this will be along the place where the grass or concrete meets the sidewalk, because that is where the water will run deeper and faster.
At the end of your waterway, put some stones to act as a landing place for your corks, so they don't float away.
Set out your bucket or pot to catch the rain.
If you'd like, decorate your water path with waterproof toys, as spectators for your race.