The Basics
Hold the Wii remote like you would a baton, with your index finger on the trigger button on the back and your thumb near the "A" button. To throw the bowling ball, hold the Wii remote upright. Bring the "ball" up to about chest level then press and hold the trigger button. Your character will begin to move forward. Swing the Wii remote backward like a bowling ball, then forward. As you swing forward, release the trigger button to throw the ball. You can move your character to the left or right by pressing left or right on the directional pad above the A button. To adjust the angle you're facing, press "A" and then left or right on the directional pad.
More Advanced Techniques
Putting spin on the ball is a useful skill to master. As you release the trigger button to throw the ball, twist your wrist to the right and the ball will go right. Twisting to the left makes the ball go left. There is a training mode mini game made specifically for mastering this skill. To have more control over the ball, adjust when you let go of the trigger button. Releasing the trigger at the very bottom of the swing puts more spin on the ball than releasing it closer to the top. The later you release, the less spin there will be on the ball.
Tips and Tricks
Several things built into the game might not be obvious but can definitely be fun. For example, you don't actually have to hit the pins in your lane. By releasing late, you can throw the ball into the lane next to yours. If you put a lot of spin on the ball, you can actually hit the pins in the next lane and they'll even count for your score. At the very beginning of the game, before you press "A" to start bowling, you can press left or right on the directional pad to change the color of your ball. In the Power Bowling mini game, it is possible to hit all 91 pins automatically by exploiting a small "cheat." By moving almost all the way to the right side and aiming at the at the railing, you can hit a small red button at the back of the lane. This will make all the pins fall over.