Whales reproduce in the same manner that humans do, by a female egg being fertilized by male sperm.
You can find out more by researching human anatomy and reproductive biology. Whales also give birth to live whales just like humans give birth to live babies and they nurse their young with milk. Different species of whales have different ways of courting their prospective mates. Humpback whales sing, the longest, strongest singer that impresses the female usuallly gets to mate with her while dolphins and other toothed whales caress each other to instigate breeding. I suggest reading Dr. Roger Payne's newest book, Among Whales, available at bookstores.