Dear Brian, This is a delicate question to answer on-line, but I will do my best. Whales are mammals and reproduce by internal fertilization just as other mammals do. To keep the animal as streamline as possible and protect them from injury, the genitals are retracted into genital slits except when reproduction is taking place. Copulation usually takes place under the water and is rarely observed by people. In general, whales are polygamous, and many males may mate with one female.
Courtship varies from species to species.
In many of the toothed whales, the males gather harems together during the mating season. After the mating season is over, the males go off alone, and the females remain together. Larger groups offer better protection for the young calves. Less is known of the mating behavior of baleen whales. Right whales have been observed in courting groups in the Bay of Fundy.