Instructions
Save your game and then speak to the clerk at the entrance of the Safari Zone. Pay the cash -- 500 pokedollars -- required to enter. You will receive 30 "Safari Balls" to use inside the zone. You can use up 500 steps or 30 Safari Balls, whichever comes first, before you must exit the zone.
Walk to the clump of long grass close to where you enter the zone, and then walk around in the grass to trigger a random encounter. Press the directions on the d-pad without holding anything down to rotate your character. This trick allows you to move your character without taking any steps. Random encounters will still trigger but, as long as your character doesn't take any steps, none will be deducted from the total limit.
Throw a "Safari Ball" at a Pikachu if one appears in a random encounter. Unlike encounters outside of the zone, you do not fight against the Pokemon to drain their health and capture them. You are able to run away or "go near" the Pokemon. Use the "run away" command if you encounter any Pokemon besides Pikachu. The "go near" command increases the chances of catching the Pokemon, but also makes it more likely to run away, so be careful. The "Throw Safari Ball" command allows you to capture the Pokemon.
Continue walking all the way left from the entrance until you reach an area with a small lake atop a hill. This is the only other area in the Zone apart from near the entrance where you are able to find Pikachus. Move in any of the spots with long grass in this area to trigger random encounters.
Reload the game if you used up your Safari Balls or steps without encountering a Pikachu. Since the encounters are random and Pikachu is rare, it may take a few tries before you are able to capture one successfully.