when you first catch a pokemon, its happiness starts at 70 out of 255.
first off, give it a soothe bell. that should cut in half the amount of time it takes for its happiness to max out. now, each of the following raises its happiness:
-using items on it, especially EV berries (21-26). i think the berries raise it by 10, but i'm not at all sure.
-giving it rare candies/vitamins
-walking 256 steps (so if you do a lot of breeding, just carry it with you next time)
-using it in battle
letting it faint, and stay KOed for long periods makes it dislike you, as do bitter medicines. and contrary to popular belief, putting it in the PC has no effect on happiness.