After the initial setup, growing plants in an aquaponics system is easy!
A Happy Medium
The greatest challenge of setup is obtaining a "grow medium" with which to fill your grow bed. Some good options include limestone-free gravel or clay balls, often called hydroton. I ended up using grow media called ViaStone because of the free shipping option at Home Depot. It works well, except for being so lightweight that it tends to float when the water level gets high, which has caused my smaller herbs to get sucked down and eventually buried by the rearranging balls of clay unless I plant them in tiny pots within my foot-deep growbed (see discussion on growbed size below). Most important is finding a medium that won't mold or break down over time, and ideally one that's smooth enough not to cut your hands when you go to plant or harvest. A less difficult but no less important challenge is creating a barrier or filter between your grow medium and your bell siphon so that your medium does not get sucked up into the siphon and stuck in one of the pipes!
Sizing the growbed
A large sterilite or other foodsafe plastic storage bin can work well as a growbed. A deep or shallow growbed can work; however, if the bed is to be less than 12 inches deep, consider adding a third element to your setup: a dark container with a lid, that will give beneficial bacteria a place to thrive. The bacteria will grow naturally, given fish waste and darkness, and convert toxic ammonia from the fish waste into nitrogen on which the plants can thrive. For ideas on how to build a system that relies on a separate container for bacteria, view this video of a backyard aquaponics setup that cost just $70 to build.
Choosing Which Plants to Grow
The only plants to avoid growing aquaponically are those such as blueberries that need a very acidic environment, since fish do best in a system with fairly neutral pH.