Well, he got to setting up a system, and today we finished it. So... aquaponics, day 1.
To answer my own question, aquaponics is the use of water and fish - with light - to grow plants. Basically, it's a nearly self-sufficient ecosystem you can put anywhere. Ours is in the basement.
We've got 8 goldfish in a 20 gallon tank of plain old water on the floor, with an air stone to oxygenate the water, and some goldfish food.
We've got a pump in with them, that spends half an hour sending water up a PVC pipe to a bed of rocks in a bin up on some cinderblocks, then an hour off to let the rock bed, which acts as the fish tank's filter, drain back into the tank and give the seeds/plants some time without being immersed.
And then the water drains back out through a PVC pipe in the bottom, back into the fish tank.
Above it all is a light fixture with two metal halide bulbs and two T5 bulbs in it.
Into the rock bed, we just sprinkled the seeds! We've got spinach, mesclun, brussels sprouts, broccoli, yellow pear tomatoes, and kale so far. We left space in the back to do some beans, peas, and cucumbers. Apparently, because of how this system is set up, the plants don't need large root systems or a lot of space, and they should grow pretty quickly.
The waste from the fish acts as fertilizer for the plants, while the plants put oxygen and nutrients back into the water for the fish. All that's needed after that is fish food. The pump is already set up on a timer, and we'll get a timer for the light, and we'll see how things go.
I'll keep you posted, of course.
The prospect of year-round fresh veggies right in our own house, though... woohoo!