Instructions
Fly to Mahogany Town using a Pidgey or another Flying Type Pokemon.
Get on your bicycle and ride west. You will eventually see Mt. Mortar, a cave with three entrances.
Enter the cave through the middle entrance.
Ask Squirtle or one of your other Water Type Pokemon to make use of his "Surf" move. This will allow you to cross the water. Continue surfing until you encounter a waterfall.
Use the "Waterfall" move to traverse the rapids. You will fall down into the basement of Mt. Mortar, where you will find the Karate King awaits.