Instructions
Put Eevee is your party. Having a Pokémon in your party will automatically begin to increase its happiness. Every step you take will add to Eevee's happiness.
Attach the Soothe Bell item to Eevee, if you have it. The Soothe Bell doubles the amount of happiness that Eevee gains.
Travel to Goldenrod City and talk to the massage therapist in the southern part of the city. You will only be able to give one massage to Eevee per day, but that will greatly increase its happiness.
Give your Eevee vitamins, such as Protein, Iron, Carbos, Zinc and Calcium.
Battle other Pokémon with Eevee, but make sure Eevee does not faint, or else its happiness will drop.
Talk to the happiness checker in Golden Rod city. When she says, "It looks really happy! It must love you a lot," your Eevee is ready to evolve. Raise Eevee's level by 1 either through battling or by using a Rare Candy to evolve it.