Hydroponics means growing plants in water without soil.
so basically the plants are growing when their roots in the water and getting all the minerals they need from from special fertilizer adjusted for hydroponic growing.
Hydroponics Methods
The Kratky Method
The Kratky method is an hydroponic technique for growing plants in a reservoir of nutrient-rich water developed by Benark Kratky from Hawaii Unuversity . in the Kratky method there is no need for electricity or pumps so it have minimal cost.
I do think that the Kratky method is the best for beginners to start with.
Nutrient Film Technique
On Nutrient Film Technique (NFT) the plants suspended in plastic containers and sometimes over long tubes. The nutrient solution flows via the tubes onto the plants’ roots and then drains back into the reservoir. On NFT you need pump
The NFT method is good for outside or greenhouse but less suited for home. I would say it’s for intermidate gardeners that gain some experiance growing on the Kratky method.
Water Culture
Water culture systems use rafts made of Styrofoam or similar material directly on top of the nutrient solution. A pump supplies oxygen to the plant roots.
The water culture method is great for growing lettuce or spinach and used buy many commercial growers.
Aeroponic
On aeroponic the roots hang in the air and are misted with nutrients and oxygen. The mistings done every few minutes.
It’s the most expensive and advanced hydroponic method and should give the best results (I didn’t try it yet so I can’t tell from my experience).