It's basically the same as breeding goldfish outside of aquaponics, except that you can't take the zero-effort route of giving them something to spawn on and then ignoring them until the survivors are big enough to notice.
The short version is:
1) give them spawning bundles to lay eggs on in spring (I've used bunches of long grass and cotton mop heads);
2) once they've laid a batch of eggs, move the bundles to a separate container to hatch and replace them (there will be more eggs. lots more eggs. so many more eggs);
3) raise baby fish.
The third stage is the most variable one - you can go from really simple (drop the bundles in a shallow pond that gets enough sun to develop microfauna for the fry to eat, ignore until the survivors are big enough to catch; most of the fry will be eaten by their older, larger siblings) to really complicated (raise microfauna to feed them, have multiple separate tanks/pools, grade fry/juveniles by size as they grow so you get the maximum survival rate). Colum's breeding adventures cover a lot of the more finicky aspects.
The main thing is that you'll need separate containers for the fry and juveniles until they're big enough to survive in your aquaponic setup. If they've got something to lay eggs on, goldies will happily
spawn in your system, but without further intervention from you it'd be a miracle if you got more than one or two surviving, if any. The adults will eat the eggs, and then the fry; the fry are basically unable to swim more than a kick or two for a couple of days after hatching, and any the adults don't eat will get swept through your system into filters and growbeds. Goldfish in ponds will breed entirely on their own and have some survive to adults as long as there's something in there for the fry to hide in, but in an aquaponic environment they need some help.