Battle with it, make it level up, keep it in your party, give it haircuts, and never have it die. To evolve into espeon, do it at day, for umbreon, do it at night.
make it happy using items
Eevee has to be happy with you at NIGHT, (you can get an Eevee from Bill's house in Goldenrod city after you reach Ecruteak city)
You have to make Eevee really happy while it's is evolving,there is no certain level that will make Eevee evolve.
Make Eevee as happy as you can. For Umbreon, level it up at night. For Espeon, level Eevee up in the day.
In Pokemon Gold/Silver you need to found Bill in his house.
just keep on training the eevee till it evolves. if u want a espeon than evolve it at day for umbreon evolve it at night p.s. im not totally sure if it works
make eevee ultra happy and level it up at nighttime in the game
get an eevee then make it happy in the afternoon or morning only then level it.
You'll need a Eevee and make it happy at night time.
You make it hold a fire-stone.
No stone evolves it into Espeon besides which Eevee only evolves in games with day time and night time features such as Pokémon Gold, Silver, Crystal, Ruby, Sapphire and Emerald. Eevee only evolves into Espeon in the day time and if it is happy enough.
Assuming you have an eevee, make it happy by giving it things from the medicine pile. Things like carbos and zinc work. You can find these in the department store in Veilstone City. Another thing to make your eevee happy is to give it massages at Veilstone City. There is a girl in a house that will ask if your Pokemon would like one. The last thing you can do to make your eevee happy is to walk around a lot!(you can check if your Pokemon is happy and likes you from the footprint dr. on the pastoria beach.) Once you think your eevee is happy, give it an exp share and battle a weak Pokemon with a strong Pokemon. In other words make your eevee level up. For umbreon, it must level up at night (after 8 to be safe). If you want espeon, make it level up in the day! Hope this helps!