Aquaponics is a form of hydroponics combined with aquaculture. You have two tanks, fish in one and plants in the other. The water is pumped from the fish tank up to the grow bed and then with gravity falls from the grow bed back into the fish tank. This process helps to benefit both the fish and the plants because while the fish poop, the plants absorb the poop. The plants receive their fertilizer from the fish (and you never need to add fertilizer) while at the same time they are keeping the water clean for the fish by removing the yuck. Aquaponics is very efficient at producing high amount of food in limited space because you get fruits and veggies from the grow bed and fresh fish meat from the tank
So here is my aquaponics system-


We have a rubber liner pond which is the fish tank


Then the grow bed is a rubber maid stock tank


The plants grow in a soil-less media, which in our case is gravel and hydroton. We have lettuce, peas, kale and parsley starting to grow. Most places claim that plants in aquaponics grow much faster than in soil and even faster than in hydroponics (aquaponics but with added fertilizer instead of fish).

As you can see in the above picture, the water is pumped into the grow bed through a pipe (see the pipe on the right) which is connected to a pump located in the pond. Then the water goes out through a pipe in the grow bed, down the stream and back into the pond.
We have started out with tilapia fish which are apparently easy for beginners but require very warm waters. they are a good eating fish and gain weight rapidly. Our plan is to eat the tilapia in fall when the water gets cool and then use channel catfish and yellow perch. Both those fish are said to do well in warm and cold waters and are commonly used in aquaponics (well catfish are anyway).
These are our tilapia


We have 25 tilapia, each 1 pound each plus a little pet gold fish.