Aquaponics is the integration of aquaculture and hydroponics. The plants and fish live together harmoniously off one another. The basics you need to know about aquaponics is that fish excrete Ammonia. Then there is a bacteria that converts the Ammonia into Nitrites. Then another bacteria converts the Nitrites into Nitrates. Nitrates are then used by the plants living in the hydroponic system. The plants clean the water and keep the fish happy because too high of Nitrite or Ammonia levels will kill the fish.
There are several different types of systems that one can construct. There are small backyard setups that operate from an ICB shipping container that is cut apart to create a fish tank and grow bed on top. There are also commercial style systems that have high stocking densities and grow lettuce and basil by floating rafts on grow channels. There is no set in stone best way to do Aquaponics. Learn the system best for you and have fun!