Once you've beaten Clair in the Blackthorn City gym, surf north into the Dragon's Den. Battle all the trainers there and get into the den itself. Talk to the elder and he will quiz you. Get it right first time to get an Extremespeed Dratini. Here are the answers:
Friend
Strategy
Strong
Love
Both
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Dratini can't learn Extremespeed in LeafGreen, but can learn it through breeding and as a prize in Crystal, HeartGold and SoulSilver. After answering all the Dragon Master's questions correctly in the Dragon Shrine, a Dratini with Extremespeed will be given as a prize.
You can surf in the Dragon's Den, or you can answer the Clair's grandfather's questions and come back later with an empty slot in your party. He will then give you a Dratini (the Dratini will know ExtremeSpeed if you answer all his questions correctly.)
You can pick whichever ones you want, though the old man won't hear you if you choose some of the 'bad' answers and he'll make you pick a different one. No matter what, you get a dratini from him (you have to leave the cave and come back for him to give it to you). But if you choose, in order, the first answer, the first answer, the third answer, the first answer, and the second answer, you get a dratini that knows extremespeed. c:
it is very rare that a furret can even learn extremespeed.
In Pokemon Gold, Pokemon Silver, Pokemon Crystal, Pokemon Heart Gold, and Pokemon Soul Silver, you can obtain a free Dratini in the Dragon's Den in Blackthorn City after defeating Clair, the Gym Leader of Blackthorn who uses Dragon-types. There is a building inside the Den where you will find a small group of elders. The head elder will ask you questions if you approach him; after they are answered, he will give you a Dratini with no strings attached. It will know Thunder Wave, Twister, and Dragon Rage. One more thing: if you answer the elder's questions with compassionate responses, your Dratini will know Extremespeed as its fourth move. If not, its fourth move will be Leer.