Misty is the first Gym Leader in the Pokemon Gold and Silver versions. Her team consists entirely of Water-type Pokémon, so it's best to bring along some Electric-type or Grass-type Pokémon to help you out.
Recommended Team
* Pikachu: Pikachu is an Electric-type Pokémon that is available from the start of the game. It can learn a powerful Electric-type move called Thunderbolt, which is super-effective against Water-type Pokémon.
* Oddish: Oddish is a Grass-type Pokémon that is available in the Viridian Forest. It can learn a move called Absorb, which will drain health from Misty's Pokémon and heal your own.
* Spearow: Spearow is a Normal/Flying-type Pokémon that is available in the Route 1 area. It can learn a powerful Flying-type move called Drill Peck, which is super-effective against Misty's Staryu.
* Zubat: Zubat is a Poison/Flying-type Pokémon that is available in the Underground Path near Mt. Moon. It can learn a Poison-type move called Bite, which is super-effective against Misty's Starmie.
Strategy
Lead off with Pikachu and use Thunderbolt against Misty's first Pokémon, Staryu. If Staryu uses Withdraw, switch to Oddish and use Absorb to heal yourself. If Staryu uses Water Gun, switch to Spearow and use Drill Peck.
Against Misty's second Pokémon, Starmie, use Zubat's Bite. If Starmie uses Recover, switch to Pikachu and use Thunderbolt.
Item Tips
Bring along some Potions to heal your Pokémon if necessary. You may also want to bring along a Paralyze Heal in case Misty's Pokémon paralyzes your own.
After the Battle
After defeating Misty, you'll receive the Cascade Badge, which will allow you to use Surf outside of battle. You'll also be able to access the Cerulean Cave, where you can encounter Mewtwo.