It would be helpful for me to know what Pokemon game you're referring to. Since the Fire Red and Leaf Green games are forward compatible, and those are the only games I know you can get one from, I will tell you where to find it :)
In Celadon City there is a place called Celadon Mansion. There you will meet a nice old lady who will give you tea. Now if you are curious enough, you will find that the mansion has a back entrance.
When you go through the back entrance you will meet a man on the top floor who (if I remember correctly) is a guru on the game or something like that. On his table there is a Pokeball. All you have to do is just pick it up, he will not object :)
That's an Eevee at level 25.
You can later breed Eevee, or any of its evolutions (you get an Eevee no matter what evolution you breed), in the daycare at Four Island after you beat the Elite 4.
In Pokemon Diamond and Pearl, you can get one from Bebe. She lives in Hearthoome City, her house is right next to the Pokemon Center. However, you have to have the National Dex before she will give you an Eevee.