Instructions
Go to Goldenrod City and find the Bike Shop. Walk north and find a lady standing near the road.
Walk up to the lady with your Eevee by your side. She will take a look at your Pokemon and gauge its happiness.
Listen to what the lady says. Your Eevee's happiness quota is between zero and 49 if she says "It doesn't seem to like you at all. It looks mean." Eevee's happiness quota is between 50 and 99 if she says "You should treat it better. It's not used to you." The phrase "It's quite cute" indicates a happiness quota between 100 and149. "It's friendly toward you. It looks sort of happy" means your rating is between 150 and 199. "I get the feeling that it really trusts you" indicates a rating between 200 and 249. And finally, you have reached the maximum happiness quota between 250 and 255 if she says "It looks really happy! It must love you a lot."