Fins, and the 'blue beard' as previously mentioned.
Females will have the more rounded, blunt fins. Males will come to a point and be more elongated. The dorsal and anal fins that is...lol
The 'blue beard' referred to is the 'heavy' blue speckling on the gill operculum and below the lower jaw. Males tend to have less speckling to almost none when compared to females.
Or you could just vent them. If its pointy, its male, round and blunt, female!
Of course there are going to be differences between species. You can't always use the same methods for sexing one species on another. It just depends on the species you are trying to sex. Some are harder than others....
Hoplarchus psittacus are pretty much only sexable by venting them or waiting till they breed. Haha.
1. The most reliable way to sex a Jack Dempsey, other than venting, is to look at the gill plate. Males will have very few to no blue speckles on the lower half of the gill plate, female will have brilliant speckled to almost solid blue lower gill plates.
2. Another fairly reliable way to sex is to look at the Dorsal and Anal (Top and Bottom) Fins. If they extend the same length or beyond the caudal fin, the fish is most likely male. It is rather uncommon for females to have longer "flowing" soft rays on the dorsal and anal fins. This holds true in many cichlid species (Green Terrors, Convicts, etc).
3. Another supposed way to sex JDs is to look for vertical band across the top of the fish. Some people believe that female tend to have dark vertical bars and males lack these. I tend to believe that the pattern is stress induced (My male had very prominent bands for the first day or so).
Males will get larger and tend to have more blue speckles across their bodies. They also tend to have "thicker" heads and larger mouths.
The most reliable way is to vent. But these methods seem very effective IMO. Good luck
FYI. The reason I put the pics in B&W is due to the fact that the picture of my male was taken with the flash off, and TrikkyMakk's gorgeous female pic was taken with the flash, so the colors are different and I did not want that to confuse people.
RDW has an awesome pair of Jacks, and the pic shows the difference between a male (bottom) and female (top)