Instructions
Play until you reach and beat the Elite Four. Walk to the fight area and look for a fisherman standing by the exit. Talk to him to receive the "Super Rod."
Return to Mt. Coronet and enter the cave with the waterfall. Use the "Surf" ability to reach the waterfall and stand next to it so that your character is directly facing it.
Press "Start" to open the game menu. Select the "Super Rod" from the backpack. Use the rod on the waterfall until your character catches a "Dratini." This process requires patience as the Dratini is not a common Pokemon.
Battle the Dratini. Use a "Dive Ball" to capture it as soon as its health is in the red.
Place the Dratini at the head of your party so that it is the first monster to enter battle. Keep fighting random encounters (by walking through tall grass) to raise the level of the Dratini. As soon as it reaches Level 30, the Dratini will evolve into a "Dragonair."