After you get your pokédex from Professor Oak, you can go north to route 1 and start catching pokémon.

Catch Some Pokémon

Go north from Pallet Town and you will see pokémon running around in the grassy area. Walk up to one of these pokémon for a chance to try to catch it. You can catch it just like you caught your starter. No need to do battle! Each time you catch a pokémon, all the pokémon in your party will get EXP. Some of the pokémon that you can catch in this area are Rattata, Bellsprout, and Pidgey. You can change their names at any time from the Party menu.

You also have access to a pokémon box, which stores extra pokémon that you don't have room for in your party. You can move pokémon to and from your pokémon box at any time.

As you go north, your pokémon might get an exclamation mark over its head and run off somewhere. Follow your pokémon and check on it, an dyou might get a hidden item.

Keep going north and you will reach Viridian City.