"Dolphin" is just the overall term used to describe that type of species of marine mammal. A female dolphin is actually called a "cow" and a male dolphin is called a "bull" much like cows. A baby dolphin is called a "calf" or "calves" for multiples babies.
As with all mammals, dolphins have two genders. Male and Female, the male dolphin mates with the female dolphin just as any other animal would. Then he give's the female dolphin sperm to fertilize her egg. Almost a year later she gives birth.