First, you have to go to Bill in Ecruteak City, meet him at the Pokemon Center, and he'll tell you to meet him at his house in Goldenrod City or something. You go to his house in Goldenrod, which is west in the city, and he gives you your cute little Eevee.
For those playing Gold, Silver, or Crystal, then:
In Pokémon Gold, Silver, and Crystal, Bill is visiting his family in Goldenrod City. After he gets the Time Capsule up and running in Ecruteak City, players can visit him at his parents' house in Goldenrod and receive an Eevee. His sister will give the player Bill's number so they can check the storage system.