Eevee can evolve into 8 different Pokemon! Here's how to get each one.

ALL EEVEELUTIONS

VAPOREON (Water)
How to evolve: Use a Water Stone on Eevee
Stats: Massive HP, great Sp.Atk
Best moves: Surf, Ice Beam, Shadow Ball, Wish
Role: Bulky special attacker/support
Rating: Excellent — one of the best Water types

JOLTEON (Electric)
How to evolve: Use a Thunder Stone on Eevee
Stats: Incredible Speed, good Sp.Atk
Best moves: Thunderbolt, Shadow Ball, Volt Switch, Signal Beam
Role: Fast special attacker
Rating: Great — one of the fastest Pokemon

FLAREON (Fire)
How to evolve: Use a Fire Stone on Eevee
Stats: Massive Attack, good Sp.Def
Best moves: Flare Blitz, Superpower, Bite, Iron Tail
Role: Physical attacker
Rating: Decent — held back by lack of physical moves

ESPEON (Psychic)
How to evolve: High friendship during daytime
Stats: Excellent Sp.Atk and Speed
Best moves: Psychic, Shadow Ball, Dazzling Gleam, Morning Sun
Role: Fast special attacker
Rating: Great — fast and powerful

UMBREON (Dark)
How to evolve: High friendship during nighttime
Stats: Amazing Sp.Def and Defense
Best moves: Foul Play, Moonlight, Toxic, Protect
Role: Special wall / stall
Rating: Excellent — one of the best walls in the game

LEAFEON (Grass)
How to evolve: Use a Leaf Stone on Eevee
Stats: High Attack, good Defense
Best moves: Leaf Blade, X-Scissor, Swords Dance, Synthesis
Role: Physical Grass attacker
Rating: Good — solid but niche

GLACEON (Ice)
How to evolve: Use an Ice Stone on Eevee
Stats: Highest Sp.Atk of all Eeveelutions
Best moves: Ice Beam, Shadow Ball, Water Pulse, Signal Beam
Role: Ice cannon
Rating: Good — hits hard but fragile

SYLVEON (Fairy)
How to evolve: High friendship + knows a Fairy-type move
Stats: Incredible Sp.Def, good Sp.Atk
Best moves: Moonblast, Shadow Ball, Mystical Fire, Calm Mind
Role: Special wall that hits back
Rating: Excellent — one of the best Fairy types

WHICH EEVEELUTION IS BEST?
Tier ranking:
S Tier: Vaporeon, Umbreon, Sylveon
A Tier: Jolteon, Espeon
B Tier: Glaceon, Leafeon
C Tier: Flareon

But all are usable! Pick the type your team needs most.