Daisy is your rival's sister, she lives at your rival's house in Pallet Town. If you talk to her she'll tell you how happy the first Pokemon in your party is (and she'll groom it for you, which raises its happiness.) If she tells you your Pokemon "can't possibly love you any more," it's at max happiness. Then just level it up and it'll evolve.
You can make your Pokemon happier by giving it a Soothe Bell and walking around with it, or giving it Rare Candies or Vitamins like Zinc and Calcium. Its happiness will go down if it faints a lot or if you give it bitter items.