Obtaining Bulbasaur: Check the house next to the Pokémon Center in Cerulean City. (Not Celadon.) You can meet Melanie there, a girl at the very back of the room. If your Pikachu is at its happiest (try feeding him Potions, even when he's at full health), talk to her as soon as you can to receive Bulbasaur.
Obtaining Charmander: Go talk to Damian northwest of Nugget Bridge. Nothing special here, if I recall correctly.
Obtaining Squirtle: Beat Lt. Surge, then go talk to Officer Jenny in Vermilion City. She'll give Squirtle to you.
Naturally, for all three, you'll need an open space in your party to accept them.