In Pokemon Yellow, the only starter Pokemon is a Pikachu. However, the three starter Pokemon from the Red and Blue games are all available in the following places:
Bulbasaur - Go to the house to the left of the Pokemon Center. Go to the girl and she will ask you to take care of Bulbasaur ONLY if Pikachu is very happy. Say "Yes" and you get a Bulbasaur.
Charmander - A boy at the north of Route 24 will ask you to take care of his Charmander. From Cerulean City, go up the Nugget Bridge. Then go to the top left corner. Talk to the boy. Say "Yes" and you get Charmander.
Squirtle - Go to Vermillion City. Now go to the lower-middle part of it. You will see an officer standing there. She will tell you that she has a misbehaving Squirtle and she wants an experienced trainer to take care of it. Defeat Lt. Surge (3rd gym leader) then talk to her again. She will ask you to take care of Squirtle. Say "Yes" and you get a Squirtle.
IMPORTANT - In all of these cases, make sure you have room in your party unless you want the pokemon to go into storage.
Chat with our AI personalities
I know you could get a Charmander in Vermillion City and a Squirtle in the route ahead of the nugget bridge. You can get Bulbasaur in a house where people are nursing a sick Bulbasaur.
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It is not possible to get all three starters in Pokemon LeafGreen without trading. This was an intended mechanic to encourage interaction between players.
No, you can only get all starters without trading in Pokemon yellow, but Leaf Green is a newer version of Pokemon green, so it's impossible.
You don't not unless you trade or cheat
By trading the other starters with other players of Diamond or Pearl.