Pokémon/Pokédex/Eevee

Flareon, Jolteon, and Vaporeon
To get Flareon, Jolteon, or Vaporeon, use the Fire Stone, Thunderstone, or Water Stone respectively.

Espeon and Umbreon
Eevee evolves into Espeon through friendship if the evolution takes place after noon; otherwise, it becomes Umbreon.

As Firered and Leafgreen do not have a built-in clock, Neither of these evolutions can occur in those titles.).

In Pokémon XD: Gale of Darkness, you can get the last two evolutions by using either a Sun or Moon Shard (not the Sun or Moon Stone) on Eevee.

Sylveon
In Generation 6 games and later, Sylveon evolves from Eevee with high affinity while knowing at least one fairy type move.

TM/HM

 * RB/Y/GS/C/RS/FL: Double Team, Rest, Toxic
 * RB/Y/GS/C: Swift
 * GS/C/RS/FL: Attract, Frustration, Hidden Power, Iron Tail, Protect, Rain Dance, Return, Shadow Ball, Sunny Day
 * RB/Y: Bide, Body Slam, Double-Edge, Mimic, Rage, Reflect, Skull Bash, Substitute, Take Down
 * GS/C: Curse, Detect, Endure, Headbutt, Mud-Slap, Sleep Talk, Snore, Swagger
 * RS/FL: Dig, Facade, Secret Power

Breeding

 * GS/C/RS/FL: Charm, Flail
 * RS/FL: Curse, Endure, Tickle, Wish

Trading Cards

 * Jungle #51 - Eevee
 * Team Rocket #55 - Eevee
 * Gym Challenge #51 - Lt. Surge's Eevee
 * Neo Discovery #38 - Eevee
 * Aquapolis #75 - Eevee
 * Skyridge #54 - Eevee
 * EX Sandstorm #63 - Eevee