Instructions
Play through the game as normal until you reach the Kanto region. This occurs after defeating the Elite Four in Johto.
Travel to Viridian Forest. This event occurs naturally in the game.
Walk around in tall grass until a Pikachu attacks you.
Battle with the Pikachu until it reaches red health. Because Pikachu is an electric-type, you must avoid using water- and flying-types due to their weaknesses to electricity. However, because you want to capture it and not defeat it, you may wish to avoid ground-types for their double damage.
Select "Item" and then "Balls," followed by the ball you wish to use. Pikachu has a relatively normal catch rate, so you should have no problem keeping it inside the ball.