Pokemon Red, Blue and Yellow at IGN: walkthroughs, items, maps, video tips, and strategies. To get Evee, just go to to Celadon City. Then go behind the pokecenter and enter a big building.
The big building is called Celadon Mansion. There are two do. Pokemon Yellow offers a few gift Pokemon throughout the game.
Some are given after a task is fulfilled, some simply by asking, and some you have to make a choice for. Generation I didn't have the breeding feature introduced in future titles, so this is the only way you can nab any of these Pokemon. Whether you're a newcomer to Pokémon Yellow or a seasoned player, this guide will help you navigate the steps needed to add Eevee to your roster.
For Pokemon Yellow Version: Special Pikachu Edition on the Game Boy, a GameFAQs message board topic titled "Best way to get multiple Eevees?". In Pokemon Black 2 and White 2, Eevee is given to the player by Amanita in Castelia City. In Pokemon X and Y, Eevee can be caught in Route 10.
I made a page on Eevee in Diamond and Pearl, but in Red, Blue and Yellow, Eevee's a bit different. Eevee can only evolve into the first 3 evolutions, Vaporeon, Jolteon, and Flareon, while the other evolutions came in later games. To get Eevee in Red, Blue, and Yellow Versions, you need to go to the Celadon Mansion, in Celadon City.
For Pokemon Yellow Version: Special Pikachu Edition on the Game Boy, a GameFAQs message board topic titled "Can you get another eevee?". In Celadon City there is a big building you can go on the roof off, go to the back entrance of the building and going into the room on the roof and in the Pokeball on the desk will be Eevee.