Either on your way out of the Dragon's Den, or if you used an escape rope or dig, in the gym, after you've taken the test.
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Go to Dragon's Den. Talk to the Dragon Den Master, which turns out to be Clair's grandfather. He will ask you some questions. If you get all the questions right (I forgot the precise answers at this moment) then, if you visit him later, will give you an ExtremeSpeed Dratini. Regardless of whether you get all the questions wrong, he will still give you a Dratini. Exit Dragon's Den and Clair will finally award you the Rising Badge, and TM59 (Dragon Pulse). Now you're ready for the Pokemon League!
In Blackthorne city there is a lady that will give you draco meteor as long as you have a dragon type pokemon
To get a shiny dratini, go to Dragon's Den (make sure you have a space on your team). Answer the Dragon Master's questions. Exit and talk to Claire, who will give you a TM (Dragon Pulse). Then go back to the Dragon Master. Before you talk to him, SAVE THE GAME. Then, when you talk to him, he will give you a dratini. Check its summary to see if it is shiny or not. If it's not shiny, switch off your DS and then switch it back on. Repeat this until you finally get a shiny dratini. (Note: this may take from as little as 5 turns to 10,000. It all depends on your luck. If you REALLY want this pokemon, just have patience and keep on trying. Remember, this could take WEEKS or even MONTHS, because the chance of getting a shiny is about 1 in 8,000+)
If youre talking about Claire than you need to go into the dragons den and pick up an item. That Item is called dragons fang.
get the dragon scale from the red gyarados and give it to mr. Pokemon or, get three matching numbers in the Pokemon lotto in the goldenrod radio tower.