1. Midline ridge: male goldfish have a ridge running through the back of pelvic fins to their vent opening on the underside. The ridge is either completely missing or smaller in females. 2. Firmness of abdomen: The area between pelvic and anal fins is pliable for females but very firm for males. 3. Shape of the vent: Though difficult to figure out, the female vent is rounder and convex, whereas the male vent is thinner and concave. 4. Shape of the pectoral fins: Male pectoral fins are pointed with stiffer leading ray and female pectorals are rounded, shorter with finer front fin ray. 5. Features: females are brighter colored and are more active. This could be a difficult way of pointing out a female but you could try! 6. Check out: One theory says that you can introduce a known female into the tank and watch for the reaction of fish. Males will check out the new fish but the females will show no interest!
The only way you can learn to spot male and female goldfish is by closely observing known males and females and noticing their various traits. A pet shop could be a nice place to learn this.