If Pikachu likes you enough, a girl in Cerulean City will give it to you.

A man in Route 24 will give it to you if you have extra space in your party.

If you defeat Lt. Surge, Officer Jenny will give it to you.

Your starter by force, and the only one available in the game

Defeat the Karate Master in Saffron City and he will let you choose one of them.

Trade Golduck for one near Fuschia City

Trade Clefairy for one near Diglett's Cave

Receive from a Sliph Co. worker after defeating your Rival.

Inside a Pokeball atop the Celadon Mansion

If you chose the Helix Fossil in Mt. Moon, you will get Omanyte when you take it to the Lab on Cinnabar. If you chose the Dome Fossil, you will get Kabuto.

Take the Old Amber you received from a man in the Pewter Museum to the lab on Cinnabar Island

One is located west of Celadon City, the other is located east of Vermillion. Use the Pokeflute to wake them up.

They are located deep within the Seafoam Islands, the Abandoned Power Plant, and Victory Road respectively.

Mewtwo is found deep within the Unknown Dungeon while Mew is found using the glitch.