The major thing with raising happiness levels is to send it out in battle all the time and to level it up. Even if you switch it out and it doesn't fight still let it participate to earn experience points. Do not let it faint, this dramatically reduces happiness. Feeding it bitter food also reduces happiness. When it gets poisoned, paralyzed, ect. then heal it straight away.
Some things that help include:
- You can take it to get a massage. There is one in Goldenrod City.
- Using berries and items such as stat increasing items (HP UP, ect.). Stat increasing items are expensive though.
- There's a girl in a house in Goldenrod City. She will inform you how much your Pokemon likes you. Go there to check your progress.
- There's an item that you can have your Pokemon hold called a Soothe Bell. It helps a lot and you can find it on the ground, behind a fence in the north of the National Park.
Have patience as raising happiness levels to maximum takes a while. Goodluck :).