Instructions
Start your Pokemon game and place Eevee at the front of your party.
Fly to Goldenrod City. Go to the Goldenrod Tunnel and visit the Pokemon Salon. Allow one of the salon's brothers to give Eevee a haircut. If it is Sunday, Wednesday or Friday, the younger brother will cut Eevee's hair for 300 Pokedollars and raise its happiness by a little bit. If it is Tuesday, Thursday or Saturday, the older brother will cut Eevee's hair for 500 Pokedollars and raise its happiness by a substantial amount.
Feed Eevee vitamins such as Calcium and Iron or berries. Vitamins can be purchased at the Goldenrod City Department Store. Berries can be found growing on many routes in the Johto region. When you take a berry, it will grow back the next day.
Use Eevee to battle trainers or wild Pokemon. Eevee's happiness will increase the more battles it wins and the more experience it gains.
Visit the house to the right of the Bicycle Shop in Goldenrod City. Place Eevee at the front of your party and speak with the lady inside. If she tells you that your Eevee looks really happy, your Eevee's happiness is at its maximum and it can evolve into Umbreon once it gains a level at night.
Train Eevee between the hours of midnight and noon until it gains a level. It will then evolve into Umbreon.