Setting up a decent-sized aquaponic system does not have to be complicated or expensive. Using a few materials that are easy to attain, you can build a barrel system similar to this one built in China.
S Stringer on YouTube shows how they had to get creative in implementing this design due to lack of materials in the area, but the end result is an extremely efficient, highly productive system.
The plants are grown in a clay aggregate in barrels cut in half. The fish are in a barrel at the bottom of the system. In the system pictured, 15 tilapia are raised in each barrel.
Water from the fish barrel is pumped up to a separate barrel suspended above the planter containers. A siphon in the upper barrel feeds water down into the planter barrels when it fills up. As the planter containers get full, the water drains back down into the fish tank.
This system can easily be expanded upon, as seen in this beautiful, larger setup installed at an area school. Anyone could use similar techniques and materials to build an amazing backyard food production system.
This aquaponics system is extremely low maintenance, requiring only daily feeding of the fish. This is a great example of an inexpensive setup that DIYers can tackle.
See the video below for more details on how the setup works and information on smaller setups built using the same concept.