In general, flying is best done by holding the Wiimote with the buttons facing up, and then rotating the Wiimote left and right to turn, while tilting up and down to gain or lose altitude. The only time you should tilt the Wiimote up is if you need to gain a lot of altitude fast; in all other cases you should use wing flaps to gain altitude.
When turning, you should never tilt the wiimote more than 90 degrees from neutral. In other words, the Wiimote's buttons should never be tilted downwards at all. Doing so will cause the game to start misinterpreting your turn direction.
The three boosts are the best way to reach top speed fast; in general you should use them as soon as they are available, and then allow them to fully recharge before using them again. The boosts are also the only way to defeat enemies in the sky, such as the wandering Guays, the Sky Octoroks, or the Skytails inside the thunderhead.
There are two ways to maintain or build your momentum while flying.
Flapping the loftwing's wings at a steady rhythm will maintain your momentum while simultaneously gaining altitude. Repeatedly flicking the Wiimote up will not work for this; instead, you have to find the right rhythm for your flicks. If you have boosts available, you can alternate them with wing flaps to increase your speed.
A dive will gain you momentum while causing you to lose altitude. A steeper dive will increase your overall speed but lose you horizontal speed, so it is not recommended to dive as steeply as possible. In general you should not use loftwing boosts while diving, as the speed gain is minimal.
The zippers are floating rocks that you can pass through to gain a large speed boost. This speed boost is far superior to the normal loftwing boost; it gives you greater speed and lasts for longer. In general, it is beneficial to make small detours to pass through these zippers when travelling in the sky.
If you use a loftwing boost as you're passing through a zipper, the loftwing boost will dampen the zipper boost, so you should avoid this wherever possible.
After you learn the Spiral Charge from Owlan, it is possible to use the Spiral Charge to pass through the randomly spawned tornadoes without being thrown from your loftwing. To do so, start your spiral charge just before you enter the tornado.