How does the Dragon shoot?

If you mean the dragon in your city then you can tap on the random monsters / marauders that appear in the city and the dragon will fly over and shoot fireballs at them.

There is also the option to build buildings that offer dragon shouts, this is once you reach level 19. These can be used against other players in the world. Once you have them you can tap on another players castle and chose the 'Shouts' option.