You simply need to have high friendship with Eevee and it will evolve into Umbreon at nighttime, just like Espeon. You can also find Umbreon in the middle of two caves between Medali and Tagree ...

Picking who to evolve Eevee into was difficult with only three options ... The two most significant examples of this are Vaporeon and Umbreon. Both of these are known for being tanky stall ...