Go to Celadon City and enter the Celadon Mansion from the rear. Then proceed to climb to the the top and enter the room.
Upon entering that room, you will see a Pokeball. This ball contains your Eevee.
Talk to Bebe inside of her house near the Pokemon Center in Hearthome City and she'll give you an Eevee. Also you can catch level 22 and 24 Eevees in the trophy garden, in order to do that you just talk to Mr. Backlot in his mansion, he will add a new Pokemon into the garden afterwards, it could be Eevee (But you can't catch Eevee in the trophy garden until you beat the elite four and get the national dex)