For those who don't read the Nihongo, here's the lowdown on how you perform all the shots. Mostly, your motions with the Wiimote mimic what you'd do with a real racket.
Swing the Wiimote from down to up to toss the ball up, then swing to serve.
Swing from lower right to upper left for forehand. Reverse for a backhand.
Swing from upper right to lower left for forehand. Reverse for backhand.
Swing from right to left for a forehand. Reverse for a backhand.
Swing the Wiimote from down to up.
Swing the Wiimote from up to down.
When presented with a smash opportunity, a star will appear on the court. Move your character over the star, then swing up to down to perform a smash.