The male goldfish have concave vents (the vents cave inwards) while the female goldfish have convex vents (the vents bulge outwards). To commence the breeding process the males and the females are first identified and then either two males and one female or three males and two females are introduced in the same breeding tank and given some time for adjustment. Soon, the male goldfishes will begin bear a lighter tint around their abdomen which would signal that they are ready for breeding. While the abdomen of the female goldfish will look slightly enlarged. One can easily notice the males chasing the female(s) during the breeding season. The females drop their eggs while the males distribute sperm over the eggs. All of this usually takes place naturally without any intervention.
However, one may also breed the goldfish artificially with hands. Hold the male goldfish and gently rub its abdomen to clear the sperm from its vent and then whirl the water a couple of times, repeat the same process as long as there is sperm left in the vent. Then hold the female goldfish and apply light pressure on its abdomen pushing the eggs out of its vent then whirl the water once more, and repeat till all the eggs are taken out. Consider mixing the water gently to properly fertilize the eggs and conclude the breeding process.