once you meet bill in goldenrod city he gives you a eevee.
You can't catch Eevee. You receive Eevee from Bill in Goldenrod City. If you want to have more than one Eevee so you can get all the evolutions, put an Eevee and a Ditto in the daycare. They will have an egg and it will be an Eevee. Also you can get one from the prize corner in celadon city for 6,666 points
To find eevee in heartgold or soulsilver, you can go to bill's house in goldenrod city, which is on the left side of the Pokemon center where the hosues are, and when you talk to him. He will give you a eevee but remember to have a space in your party or you won't be able to get it until you do.
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Breed in the daycare with ditto
you have to go to goldenrod city and go to the house near game corner talk to bill and he will give you a level 5 eevee
You have to use a leaf stone on your eevee. Sorry, I don't know where to find a leaf stone though. : ) hope this helped!
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You can't find Eevee in Pokemon Ruby, but you can trade for it from Fire Red, Leaf Green, and XD.