Raise its happiness. You do that by walking around with it (A LOT) and giving it potions. Battling with it also helps but be careful not to let it faint. Once it is happy enough (and you level it up), it will evolve into Espeon during the day. At night, it'll become Umbreon.
It takes patience though and the results for people vary. I got my Umbreon at lvl 31 =/