It depends on the story or legend. LOL!!! Consider this...Most dragons breed in the early spring. Male dragons keep their testicles tucked inside their body so it can be hard to know if a dragon is a male or a female. When a male dragon spots a female that he wants to mate with he will go to her directly from the side rather than mounting himself on top of her. He may dance around in an effort to try to attract her. When the male dragon is close enough to the female dragon he will then take hold of her by biting her on the neck. He will then be able to hook onto her with his hemipenes. These are like hooks that connect to the female. After this he will ejaculate his sperm through his penis and hemipenes and into the female dragon. She may even save some of the male's sperm in her body to fertilize more eggs in the future without having contact with that particular male again. Keep in mind that this process can be performed in mid-air if the dragons fly. If they are flightless and snakelike they coil together until finished.
After a female dragon is fertilized she will start to make her existing nest more comfortable or she will start making a nest, depending on the species of dragon. She will find a very private spot to lay her eggs to avoid predators. Some female dragons like to dig holes or create a rock nest, inside a cave or deep cavern. The eggs usually hatch within 50-55 days, depending on the type of dragon, because some dragons simply give birth to their babies at this time. When the baby dragons are born they are able to take care of themselves right away. They learn everything they need to know on their own and they typically never meet their mother or father.