Hydroponics
This is a method of growing plants without putting them in the soil. Instead, they are grown in a liquid solution, as the name suggests. This solution should contain nutritive elements essential to the plants development. Obviously the solution must contain nitrogen, potassium and phosphorous, but plants also require trace elements like iron to survive in this enviromnment.
It is advised to use fertilizers specially made for this method of growing, as they are corrrectly dosed and willl not burn the roots of the plants.
The roots also feed on the oxygen in the liquid. To increase the amount of oxygen, you can install an aquarium pump to generate movement on the surface of the water - this agitation will oxygenate your solution.
Finally, you can also use clay or glass marbles, stones, or stakes to keep the plants upright, filters for the aquarium,etc....