Cut the top off of the soda bottle. Make the hole big enough for a cup fit into it without going all the way through.
Cover the edges of the soda bottle with duct tape. This helps to hold the cup, plus keeps you from getting cut on the sharp plastic.
Poke small holes around the lower sides and in the bottom of the Styrofoam cup. The roots will eventually grow through these holes and into the nutrient solution.
Fill the cup with perlite and plant a seedling in it. Get the perlite wet, then place the cup into the bottle. The level of the nutrient solution should be high enough to flow into the holes in the cup until the roots of the plant grow out of the cup and into the liquid.
Keep the level of the nutrient solution an inch or two below the bottom of the cup once the roots can reach that far.
Cut the sheet of Styrofoam to fit the wading pool, with a small gap on all sides so that it is able to float freely.
Create several holes in the Styrofoam that are large enough to hold the net pots so that they reach into the hydroponic solution, but small enough that the pots won't fall through.
Fill the wading pool with nutrient solution. You can make your own or buy a commercial version intended for hydroponic systems.
Place a single seedling in each net pot. Arrange them so that they are supported and able to stand up in the pots.
Float the Styrofoam sheet on the liquid in the pool. Put one of the net pots with a seedling into each of the holes cut into the Styrofoam.