Make sure Eevee has at least 2 hearts of friendship with you
Feed Eevee 1 of the following: Poké Beans, or a Poffin (best option: a Poffin)
Walk with Eevee until friendship increases (or use Super Training/refreshing methods in your game)
Evolve Eevee at night (in-game time)
Use the Evolution option to evolve Eevee into Umbreon
If it doesn’t work, increase friendship further and try again at night