All of these will raise happiness:
Levelling it up
Giving it Vitamins
Giving it one of the five EV-reducing Berries (Emerald only)
Using it in your team when you battle a Gym Leader or the E4
Walking with it in your party (every 256 steps, your Pokemon's happiness has a 50% chance of increasing)
If you walk around with or level up a Pokemon in the area it was caught in, its happiness will raise more. Also, the Soothe Bell multplies changes in your Pokemon's happiness by 1.5 when its holding it.
All of these will lower happiness:
Letting it faint
Giving it a bitter heal item (Energypowder, Heal Powder, Energy Root, Revival Herb)
Trading (its happiness will "reset" to the default)