Instructions
Find an Eevee. Eevee's location switches between games, but the creature has always been given to the player as a gift. You can never find an Eevee in the wild. For example, in "Pokemon FireRed" and "Pokemon LeafGreen," the player receives an Eevee by entering the Celadon Mansion from the rear entrance.
Raise the happiness level of Eevee. There are several ways to improve Eevee's happiness, including feeding it expensive vitamin items such as Iron and Carbos, going on long walks with Eevee and leveling it up.
Level Eevee up at night when its happiness is at a high level to evolve it into Umbreon. Night starts at 8 p.m., and as long as Eevee is happy, it will turn into Umbreon. You can check Eevee's happiness by taking it to someone in the game who can tell you a Pokemon's happiness level. In "Pokemon Black," a woman in Nacrene City can tell you the current happiness level of any Pokemon in your party.