To evolve Eevee into Umbreon you need to make it really happy and level it up at night and it could potentially evolve at any level in order for it to evolve into Umbreon except for Level 10. Ways to make it really happy include having it in your team a lot or feeding it nutrient stuff like Protein, calcium, etc. Night time in-game time varies depending on the Pokemon game however for HeartGold and SoulSilver night time is between 8 PM and 4 AM additionally walking with it, making sure it doesn't faint, feeding it berries that it likes are also ways to raise its happiness.
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To evolve Eevee into Umbreon max out its happiness at night. Having it first in your party while holding a soothe bell, having it battle a lot, or feeding it many rare candies are all ways to help it evolve into Umbreon. ~KKMG1
To get an Espeon level Eevee with high happiness during the day(10:00 AM to 5:59 PM). Having Eevee first in your party while it holds a soothe bell, feeding it many rare candies, and battling with it often are all ways to increase its happiness. Though you have to be careful if it levels at night with high happiness it will evolve into Umbreon.
You cant evolve it into glaceon unless you bring an ice stone over from a game that has more stones than silver, (silver doesn't have to many.) after transferring it, eevee will evolve. The best you can do without an ice stone is espeon(if it evolves in day) or umbreon (if it evolves in night).
You can't evolve Eevee to Espeon with a stone. There is something called happiness points. The more you train the Eevee, the happier it becomes until eventually it evolves normally in the day. If it evolves at night, you get an Umbreon instead. You can't tell how many points it has, but i guess it eventually evolves.
he has 8 evolutions jolteon,flareon,glaceon,espeon,sylveon,leafeon,umbreon and vaporeon.