After you win the Cascade Badge from Gym Leader Misty, go north from Cerulean City to Route 24.
Battles on Nugget Bridge
At the entrance of Route 24, you will find a golden bridge, known as Nugget Bridge. There are five trainers on this bridge.
Go north and you will battle Bug Catcher Cale. He has a level 9 Venonat. You get 108 Pokédollars and 3 Poké Balls for winning.
Go north to battle Lass Ali. She has a level 10 Psyduck. You get 200 Pokédollars and 3 Poké Balls for winning.
Go north and you will battle Youngster Timmy, who has a level 10 Sandshrew. You get 200 Pokédollars and 3 Poké Balls for winning.
Farther north, you will battle Lass Reli. She has a level 10 Meowth. You get 200 Pokédollars and 3 Poké Balls for winning.
Keep going north to battle the fifth trainer, Camper Kevin, who has a level 11 Growlithe. You get 220 Pokédollars and 2 Great Balls for winning.
After the battle, go north and you will get a Nugget from the mysterious Trainer. Then you have to battle a Team Rocket Grunt who has a level 11 Zubat and a level 11 Koffing. You get 308 Pokédollars for winning.
Explore the Route
Go west, then south, to find some grass, where you can encounter wild Bellsprout, Meowth, Venonat, Pidgey, Squirtle, and others.
You can battle Camper Shane in this area. Shane has a level 11 Spearow. You get 220 Pokédollars and 2 Great Balls for winning.
Go south from Shane to get 3 Razz Berries.
To the north, there is a trainer who will give you a Charmander if you have caught at least 50 pokémon.
Go east from here to reach Route 25.