In Pokemon Gold/Silver you need to found Bill in his house.

Go to Hearthome City and go to the house next to the Pokemon Center after obtaining the National Dex. Inside the house is Bebe who is going to ask you to obtain the Eevee, say "yes" and she'll give you Eevee as long as there's at least one empty slot in your Party. You can also find Eevee in the Trophy Garden after getting the National Dex and talking to Mr. Backlot. He may tell you he found a Eevee in the garden.

You can get an eevee if you go up to the man who is outside professor rowens lab and talk to him he will then say My friend is ... and he will tell you where to go you talk to the lady and make sure you only have 5 Pokemon in your handthingy she will ask you if you would like the eevee.

yea..

Eevee can be found on the roof of the Pokemon Mansion in Celadon City. You have to go around and use the back entrance, though, to get to the room where you find it.