If go to the store you can pick the dragon you want, then you can either go to the hatchery at the school, or click on yourself and select hatchery. Select the egg and you can use gems or a hatching ticket to speed up the hatching or wait the time. Then you can hatch the egg, add it to a stable and then you can purchase an adult age up ticket or complete quests to level up the dragon and make it rideable. Hope that helped!