How do you get dratini in Pokemon Silver?

Dratini is found in three places in Pokémon Silver Version. It can be caught by Surfing (10% chance) or Fishing (10% chance with the Good Rod, 30% chance with the Super Rod) in the Dragon's Den; by Fishing (same odds) on Route 45; or by paying 2100 coins at the Goldenrod Game Corner.

If you are playing the Generation IV remake, Soul Silver, all of the above is still accurate for Dragon's Den and the Game Corner. Dratini is no longer found on Route 45, however; instead, it can be found by fishing in the Swamp area of the Johto Safari Zone.