There are a few ways to increase Happiness.
but be careful, for doing these will decrease their Happiness:
Chat with our AI personalities
Makes your pokemon's happiness go up faster.
Go to Vendanturf town Talk to the lady in the house beside "Wanda's House" Note: the Pokemon that you want to check it's happiness must be in front of the line.
Maxing out the happiness of a pokemon is somewhat time consuming. Walking around with the pokemon in the lead position will help slowly increase the happiness. You can also feed the pokemon poffins to help raise stats and happiness.
To evolve Eevee into Espeon in Pokemon Emerald you need to raise it's happiness to max and level it up during daytime. To raise happiness you can keep the Eevee in your team for a while and fully healed up it should eventually reach max happiness to evolve in the daytime.
Level up an Eevee with full happiness at nighttime (after 6pm)