Umbreon is the dark type evolution of Eevee. It's one of Eevee's final forms, the others being Vaporeon, Jolteon, Flareon, Espeon, Leafeon, Glaceon and Sylveon. Eevee evolves into Umbreon when it levels up at night and has a high level of happiness.
Obtain an Eevee
The first step is to obtain an Eevee. In each Pokémon game there are different ways to obtain an Eevee. In Pokémon Fire Red and Leaf Green one can be found in the Celadon Mansion. In Pokémon Diamond, Pearl, and Platinum, there are wild Eevees in trophy garden. In Pokémon X and Y there are wild Eevees on route 10.
Raise Your Eevee's Happiness
Eevee will only evolve into Umbreon if its happiness is high. The best ways to raise a Pokémon's happiness are to level it up, feed it many berries or poffins, or play Pokémon-Amie with the Eevee.
Once Eevee has a high happiness, it will evolve into Umbreon under specific circumstances. If Eevee is leveled up at night time, it will evolve into Umbreon. You can also adjust the clock on your gaming system to make it night time if you don't want to wait to evolve your Eevee into Umbreon.