Instructions
Give Eevee the Soothe Bell for a hold item. The Soothe Bell is found in National Park and will cause Eevee to earn twice the amount of happiness points.
Give your Eevee MooMoo Milk and Lemonade. Buy MooMoo Milk from the Pokeathlon Dome or the Miltenk Farm on Route 39 for $500. Lemonade can be purchased in the Pokeathlon Dome or from shops in Goldenrod City, Celadon City and Mt. Moon for $350.
Feed your Eevee its favorite foods. Eevee likes foods with the sweet flavor rating, so feed it Poffins made from sweet berries such as Pecha, Oran and Sitrus berries.
Give your Eevee vitamins such as Protein and Carbos. Every vitamin in the game has a different effect, but each will give your Eevee an increase in happiness.
Check your Eevee's happiness by looking at your Poketech application from your trainer menu. If your Eevee shows two hearts above its head, it is at maximum happiness. Level up your Eevee with maximum happiness during the day by battling other Pokemon or giving it a Rare Candy and it will evolve into Espeon.