After exploring Celadon City, you cut down the tree blocking the path to Celadon City Gym, a Grass-type gym.
Enter the Gym
At the entrance, show the Lass your partner pokémon (Eevee or Pikachu) to be let in.
Follow the path into the Gym, and you can battle Lass Kay, who has a level 28 Oddish. You get 560 Pokédollars for winning.
Continue along the path, and you will reach a dead end with some vines to the north and to the south. You can chop down the south vines for a shortcut to the exit, or chop down the north vines to continue through the gym.
After going north from those vines, you can go east, then south, to battle Beauty Mai, who has a level 29 Exeggcute. You get 1740 Pokédollars for winning.
From Mai, go north, then west, then north. Go east and you can battle Picnicker Tina, who has a level 29 Gloom. You get 580 Pokédollars for winning.
Go west from Tina, then south when the path splits, then go east to battle Beauty Tamia, who has a level 29 Oddish and a level 29 Weepinbell. You get 1740 Pokédollars for winning.
Go west, then north when the path splits. You will reach two sets of vines. You can chop down the east vines for a path back to the exit. Chop down the west vines to continue through the gym.
After going west from those vines, you can battle Beauty Lori, who has a level 29 Gloom. You get 1740 Pokédollars for winning.
From Lori, go south down the path near her, and follow the path. You can battle Ace Trainer Mary, who has a level 31 Weepinbell and a level 32 Tangela. You get 3200 Pokédollars for winning.
Go north up the path near Mary. To the northwest, you can battle Lass Lina, who has three level 28 Bellsprouts. You get 560 Pokédollars for winning.
There are two sets of vines south of Lina. Chop down the vines on the left for a path to the exit of the gym. Chop down the vines on the right to go farther through the gym. After going down the path on the right, you find two more sets of vines. Chop down the vines on the right for a path back to the exit. Chop down the vines on the left for a path to the gym leader.
Gym Leader Erika
Erika has a level 33 Tangela, a level 34 Vileplume, and a level 33 Weepinbell. You get 5440 Pokédollars for winning. After the battle, Erika gives you a Rainbow Badge, which causes pokémon from other trainers to listen to you if they are level 50 or lower. She also gives you TM53 Mega Drain.
After the Gym
Now that you have the Rainbow Badge, you can buy Ultra Balls, Hyper Potions, and Super Lures at Poké Marts (and the Trainers' Market in the Celadon Department Store).
Next, you should go to the Rocket Game Corner.