Evee???

You receive it on the top floor of Celadon mansion

I believe that you recieve an Eevee on the top of Celadon Mansion. I think there is a pokeball on a desk.
Or you can breed a Flareon,Jolteon,Vaporeon Etc.

You can:

A) Breed Espeon, Umberon, Flareon, Jolteon or Vaporeon to get a baby Eevee.
B) Go to the Celadon Mansion's top floor and recive one.

I will see if I can explain to you exactly how you can get your hands on an Eevee. Because, it can be pretty confusing.

Alright, first you have to be kinda far in the game. I mean far as in, you are in Celadon City, or past Celadon City. If you are not yet in Celadon City in Pokemon Fire Red, then I suggest that you work on getting there first because that is where you find your Eevee. When you first arrive in Celadon City, head north till you reach a small path that takes you behind the buildings. Look for a big building that is near the Department store, and you should see a entrance to the back of the building. Go inside the building, and you will notice that you are Cut off from the rest of the building, and people. Just proceed to the very top of the building by going up all the stairs on each floor. You should be able to enter a small building on the top floor, and inside will be a table with a Pokeball on it, as well as a big man nearby. Talk to the man, and then if you have an empty space in your Pokemon Party, you can take the Pokeball, and the Eevee inside of it. Hope this helps.

To get an eevee, first go to Celadon City. Then go inside the huge building near the Department store(I think you need to enter from the back, if not, the front) and go to the roof. There will be a small room there. Go inside and you will see a pokeball on the table. Take it and you have got yourself an eevee!!

Go to the one town where there is a tall building like a mall. On top of one of the building you need to go to the back side of it and go through the door. Once you do, go up the stairs and to the top floor. In the only room up there, there should be one.