Instructions
Get a fishing rod if you do not yet have one. Head to Route 32, south of Violet City. Continue walking south until you come close to the end of the path, near Union Cave.
Enter the Pokemon Center. Speak to the fisherman on the first floor to receive the Old Rod. This basic rod catches Pokemon like Magikarp, Tentacool and Staryu.
Leave the Pokemon Center. Find a body of water, such as the nearby ocean by the docks.
Face the water and press the "A" button. A message appears, asking if you want to fish. Select "Yes."
Wait for a few seconds. If you catch something, a battle with the wild Pokemon starts immediately. If you catch nothing, a message appears to let you know that fish are not biting in this area.