Dave started a thread in the permaculture forum about this:
The thread "Aquaponics" in
Permaculture forum
You can find a few of my pictures of a system I was using at the time in there. I've done various aquaponic systems, using floating rafts, flooded media, flood and drain both timed and siphon-regulated, vertical towers, dutch buckets, nutrient film (NFT) and shallow wicking. I've used tilapia, koi, goldfish and others as aquatic livestock. I've been diverting fish water for plant growth for twenty years, but it's only been in the last twelve or so that I've been returning the water back to the fish afterwards. It seems like most hydroponic equipment and methods can be adapted to aquaponics, but some of it requires a lot of filtration to keep sediment from clogging things up. I don't think NFT or the aeroponic methods are well-suited to aquaponics, but some people disagree with me.