Actually set up an NFT (nutrient film technique) recently (adding plants this weekend) and done a lot of research before setting it up on my 55. Aquaponics uses in what would otherwise be considered overstocked tanks by most aquariests standards (fish end up being food rather than pets in most cases but plenty of people use 'pet' catfish (pleco) and goldfish as big waste producers to feed their plants (also seen on large heavily populated cichlid tank). The plants get nutrition from the water from fish waste (through nitrogen cycle) and fish foods most people in aquaponics use to help added needed nutrients. Iron seems to be the main thing people add to the systems as and there has been several threads/sites that cover different types of iron supplements to sue depending on your pH (as some will not be properly absorbed at higher pHs.
Hydroponics utilizes a lot of supplement additives and is very precise, aquaponics is more 'free form'/'nature takes it course' you could say and not so anal about nutrients.
Keep looking up aquaponics on youtube, there's a ton of helpful and informative videos.
added info: as for adding to an existing tank many use a single pump in tank (or canister filter if pre-exsisting like mine) pump water up from tank to aquaponics system above tank (usually grow beds) and use constant fill (with bell siphon) or ebb and flow method (pump on a timer + bell siphon or simple drain) siphon drumps water right back into tank with gravity. Some people use 2 pumps and have a sump system added in, I don't like the idea of one pump can fail and you end up with a drained tank and a giant mess.
Look up aquarium aquaponics or something simular on youtube, plenty aquarium based videos from small betta boxes to large aquariums.
I am using a simple setup over my 55 gallon tank with my poop monster pleco as the nutrient producer. I actually set this system up (with huge help from hubby) to help keep nitrates lowered in the tank, added bonus is getting food we (or the pleco) can eat ^^. Mines a small NFT system using pvc tubing (6 openings for plants in it), connected outflow from canister filter to one end, have other end (past plants) dump out into the tank with a 90* elbow and shut off valve to control how high water is in the tube.
Went with nft to avoid grow bed siphons turning on and off, since the system is inside and in a room below the bedroom, don't want to hear it go on and off (it gets quite loud) as you may notice from watching videos of aquaponic setups using bell siphons.