Things You'll Need
Instructions
Begin the game, and travel to the Lake of Rage. Use your Pokemon's "Surf" ability to surf to the middle of the lake and encounter the Red Gyarados.
Catch the Red Gyarados by weakening it with attacks from your other Pokemon, then throwing Pokeballs at it until it is caught.
Surf around the lake after catching the Red Gyarados and catch a normal Gyarados using the same method from Step 2. Make sure this second Gyarados is the opposite gender as the Red Gyarados.
Take the normal and red Gyarados to the Pokemon daycare center on Route 34, south of Goldenrod City. Give the two Gyarados to the daycare center owner, and wait for the two Pokemon to breed.
Take the egg from the daycare center after your two Pokemon have mated. Walk around with this egg until it hatches, producing a Golden Magikarp.