Eevee is the one Pokémon in the games that sets itself apart. Why? It has 7 different Evolutions.

However in the 3rd generation, 2 of it's evolutions, Espeon & Umbreon, were deemed by many to be impossible to get.

So when Pokémon Colosseum came out, one of the options was clear. You started off with both Espeon & Umbreon and you could trade them back to your game to get them, plus in XD, you are able to evolve your Eevee into them using Sun & Moon Dust. However Espeon & Umbreon are obtainable in other ways, contary to popular belief. Either you trade the above and breed to get an Eevee on your Ruby, Sapphire or Emerald game or you trade an Eevee or it's evolution over from FireRed or LeafGreen. Either way, you need an Eevee on Ruby, Sapphire or Emerald

Now to get Espeon, you have to totally max out Eevee's happiness. Then once you have done that you MUST raise it one level at the following times; between 12pm and 12am
But to get Umbreon, you have to totally max out Eevee's happiness. Then once you have done that you MUST raise it one level at the following times; between 12am and 12pm

And there you have it, that is how you get Espeon and Umbreon in the games...those are the time set evolutions and you can easily trade them onto FireRed/LeafGreen. However, in Diamond & Pearl, you can get them in Daytime and Nighttime respectively.

The only games you can get Espeon & Umbreon are:

In Diamond & Pearl, the above issues are rectified as both Day & Night time have been returned to full forse so in the Day & Evening you can get Espeon, but once it hits Night, you will get Umbreon. However, Diamond & Pearl brings two new evolutions of Eevee to the fold, and the ways to get them are well hidden, you aren't likely to find it out unless you're incredibly lucky, or you read it here. This cannot be done on HeartGold or SoulSilver so you'll need to trade your Eevee over to Diamond, Pearl & Platinum to evolve it into these Pokémon

The first new evolution of Eevee is Leafeon, a Grass type form of Eevee. How do you evolve it? Well it is not by Happiness or through a Stone. What you need to do is go to the Moss Rock in Eterna Forest in Sinnoh or the Moss Rock in Pinwheel Forest in Unova. Once there, do a few battles until your Eevee levels up. Once its levelled up, it should evolve into the Grass Type Eevee; Leafeon:
The other new evolution of Eevee is Glaceon, a Ice type form of Eevee. How do you evolve it? Like Leafeon, what you need to do is go to the Ice Rock in Route 216 in Sinnoh or the Ice Rock in the Twist Mountain in Unova. Once there, do a few battles until your Eevee levels up. Once its levelled up, it should evolve into the Ice Type Eevee; Glaceon:

The only games you can get Leafeon & Glaceon are: