Strong fundamentals will take you a long way with Haku.
I find he works best as an anti-offense character. You have counters, and then you have great normals that fish CHs. With a bit of work, you can always keep them guessing, and he's got decent abare to keep up momentum. Spacing is also key. Shutting down the other guy is one of Haku's strengths. Use it.
Most combos require 3 stars or less. His high-dmg stuff doesn't need more than 5. He averages 3k+ midscreen, 4-5k in the corner, and 6-7k+ at top end. Very decent output. He's also got some of, if not the, best corner carry combos since they go full-screen or close to it. On top of that, most combos can be started from just about any normal.
Any questions, we're all here to help.