Hydroponics is the cultivation of plants without soil, in water containing dissolved nutrients. Essentially, a nutrient solution bathes the roots and fertilizes the plants in the absence of soil and allows them to grow. There are several systems that can be used to grow hydroponic plants; a simple system isn't very difficult or expensive to set up.
Rinse the aquarium well and paint the outer surface of the aquarium black, or cover it with aluminum foil to keep out any light that would encourage algae growth.
Prepare the hydroponic fertilizer solution according to the package instructions and add to the aquarium.
Check the pH level (a measure of the acidity or alkalinity) of the solution with a test kit and adjust as necessary according to the package instructions. Usually, a pH between 5 and 6 is appropriate.
Connect the aquarium air pump to the tubing and aerator (air stone) and place the aerator in the water inside the aquarium (the air pump packaging should indicate what size tank it will work with).
Cut the foam sheet to a size that will rest on top of the aquarium. Trace around the net cups (or use small plastic drinking cups pierced with many holes) onto the foam sheet. Cut out holes in the Styrofoam sheet with a box cutter to hold the net pots (or perforated cups) in place.
Slip a net pot or perforated cup filled with growing medium into each hole until the lip rests above the surface of the Styrofoam sheet. The number of spaces created will depend on what crop is grown---be aware of how much space the plants you are growing will need as they mature. The bottom half of the net pot (or perforated cup) should be below the level of the nutrient solution.
Plant 1 or 2 seeds per net cup, about ¼inch down, covering slightly with growing media. Be sure that the growing media is moistened with nutrient solution. Switch on the aquarium pump and leave the seeds to germinate.
Keep an eye on the nutrient level---be sure to maintain the original level of the solution over time, adding water as necessary. Change the nutrient solution every two weeks, being very careful to not disturb the delicate, developing roots.