That's all pretty straight-forward. Motion controls come into play when you encounter an enemy. Your standard attacks are unleashed by waving the Wii Remote - any indistinct shaking motion seems to do the trick. This basically replaces the mashing of a face button, which is nothing too advanced.
If you played Two Thrones you will remember that some enemies, when defeated, will drop weapons that you can actually pick up and use in your other hand. When you're duel-wielding blades the Nunchuk can be wiggled along with the Remote to attack with both weapons.
The Prince's deadly Speed Kills also make use of the Nunchuk motion sensors. Just like before, if you manage to sneak up close to an enemy without being spotted, the screen will blur around the edges to indicate a Speed Kill opportunity. At that moment, shoving the Nunchuk downwards will activate the Speed Kill animation which sees the Prince grab his victim to deliver the fatal blow.
To succeed in your attack, you must wave the Remote at the right moments during the Speed Kill cutscene - usually just as the Prince draws back his knife - to initiate the blow. It's the same as before but, again, this version replaces the press of a button with the shake of the Remote.