Well.. We're starting with a basic walkthrough of how to get each Eeveeloution! Some data might be incorrect, due to the fact this is what I'm hearing from most people.

Kanto Eeveeloutions

Flareon - Use a Fire Stone on a Eevee

Vaporeon - Use a Water Stone on a Eevee

Jolteon - Use a Thunderstone on a Eevee

Johto Eeveeloutions

Umbreon - Level up at Night

Espeon - Level up during the Day

Sinnoh Eeveeloutions

Leafeon - Bring a Eevee to a Mossy Stone.

Glaceon - Bring a Eevee to a Frozen Stone (whatever it's called)

Kalos Eeveeloutions

Sylveon - Level up with a Fairy-type move and 2 Affection... (not sure about this one)

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I hope this helped! This is Umbreon-kun signing out!

~ @UltimateUmbreon