How do you find male and female fantail goldfish?

Determining the gender of goldfish is a lot harder than people may suspect. During breeding season, the males will get what we call breeding stars on the cover of their gill plates; they look like tiny white bumps.
You might also be able to tell by their vents under their tail, but it takes a lot of practice and knowledge to easily tell them apart when it's not breeding season.

In addition, even if it is breeding season, and you have all males, or all females in your tank, it remains difficult to tell the difference as the males need a female in the tank, and vice-versa for the females so that they will show typical breeding behaviour.