Ok,the first thing you need to do is go to the tutor house in the route between Solaceon Town and Celestic Town.Next you can see a house where you can access by using the HM Rock Climb.You use it twice to get to the house.The second time you use Rock Climb,there is a Dragon Trainer that will challenge you.(If it's your first visit.)He has a around Lv.30 Gible.
Once you beat him.You can go to the house.Once inside,you'll see an old woman.She is the Draco Meteor tutor.Your Dragon-Type Pokemon has to have high or max happiness.You can check on how happy it is by the Pokemon happiness app for the Poketch.You can find it in Eterna City Pokemon Center.An Aroma Lady gives it to you.Or Dr. Footsteps near Pastoria.
(Is my answer to long?)