Eevee's happiness level must be at least 220 for it to evolve into Umbreon.
To check your Eevee's happiness, go the the southwestern-most house in Verdanturf Town and talk to the lady inside. When she asks if you want her to evaluate your Pokemon's happiness, press yes and select Eevee.
If she says
"It seems to be very happy. It's obviously friendly toward you."
"It's extremely friendly toward you. It couldn't possibly love you more. It's a pleasure to see!"
you can evolve your Eevee, you just have to level it up during the night.
If she doesn't say one of those things, you need to raise it's happiness higher.
(Note: This is for ORAS, you can find what the Happiness Checker says and the Happiness Checker location in my sources)
Hope this helps!
Happiness Checker location
Happiness Checker sayings