Instructions
Head north from Pallet Town towards the Viridian Forest. Be sure that your current Pokemon is strong enough to survive and not faint in the forest. Go back to the Pokemon Center and heal if necessary.
Walk around grassy areas in the Viridian forest until you encounter a Pikachu. Note that it is rare and will require some time before you will see it.
Use your given Pokemon (Charmander, Squirtle or Bulbasaur) to weaken Pikachu until its health is in the red region. You will have a harder time if you choose Squirtle to be your given Pokemon, as it is a water type and weak against an electric type like Pikachu.
Throw a Poke Ball at Pikachu until you catch it. When successful, you will have your very own Pikachu as a starter Pokemon before even battling the first gym leader.