Umbreon is the Dark-type Eevee evolution. You can obtain this Eeveelution by leveling up your Eevee during the night with over 225 happiness. This can be achieved by gaining XP from a battle or using a Rare Candy. This will only work during the night, not in dark areas. So don't try evolving your shiny Eevee into an Umbreon in a dark cave in the daytime. You'll get an Espeon.
To make an Eevee happy you have different options: