In the text below I shall try to give a short overview of some of the basics when breeding crayfish. Particular species may have other behaviours and demands. It should be said that my main experience as an aquarist is with relation to fish, but I shall try to convey what little knowledge I have.
Sexing crayfish isn't always easy. The genital openings are located in different places on the body depending on whether it's a male or a female. Males have their genital openings behind/under their posterior pair of legs. Females have their genital openings under the third pair of legs counted from the posterior. However, many individuals have a male as well as a female genital opening, making the sexing much more complicated. But these are always either male or female; usually male but you can't be sure.
Mating and egg carrying
In aquariums, spawning is possible any time of year. The male makes a little sperm packet and places it on the female's stomach. The female then spawns her eggs, passing them through the sperm packet so that the eggs get fertilized.
It is not uncommon for the female to lose a claw during this process. She then places the eggs under her tail where they will be kept until they are ready to be released. How long this will be depends on the water temperature and the species, but it will be at least 4 weeks. A lot of other factors can also affect the length of the egg carrying period, such as water quality, and food supply and quality. The mother will watch over the young for a short time after birth.