Video Link: https://www.youtube.com/watch?v=tmKkuf9_5CU
It can sometimes be tricky to tell the difference between male and female goldfish, but there are a few different indicators you can use. Taken individually, each one can be a little unreliable, so it's best to consider them as a whole when trying to determine the sex of your fish. And of course, the most reliable way is to actually witness your fish spawning.
Breeding stars or tubercles are small white nodules that appear on the rays of the pectoral fins, on the operculum and face, and sometimes even on the body of male goldfish. In some rare cases, breeding stars appear on female goldfish too, but mostly they appear on males. If I see a fish with breeding stars, I automatically assume it’s a male until proven otherwise, because it is so uncommon in females. Here is my video all about breeding stars with lots of examples and good information.
Typically males have a more elongated and narrow vent, while females have a rounder vent. Male vents also tend to be “innies” or concave, while female vents tend to be “outies” or convex. You can typically see the convex female vent from a side-view.
This is probably the most unreliable method for fancy goldfish since they have such a modified body shape. But in general, females have a wider and deeper body when compared to males of the same type. Sometimes they also tend to have an asymmetric belly when viewed from above. Males tend to have thicker leading rays on their pectoral fins.
And finally, you can observe their behavior around spawning time. A few weeks before spawning, males will start chasing or following females around. They usually stay just behind and below the female while chasing. Chasing will become more obvious as spawning approaches, and when they do start spawning, the male will chase and sort of “push” the female into soft plants where she will then lay the eggs while the male fertilizes them. Here is a video showing some butterfly telescopes spawning.