To evolve an Eevee:
To Flareon, use a Fire Stone (any time of day).
To Vaporeon, use a Water Stone (any time of day).
To Jolteon, use a Thunderstone (any time of day).
To Espeon, make it very happy, then raise it one level during Morning or Daytime.
To Umbreon, make it very happy, then raise it...