While the story may seem a little complex, the actual game structure is surprisingly simple: Kill nine dudes. Yep, that's it. But before you can start the slaying, you must perform various investigations in order to gather the adequate information for each hit. You gather information in several different ways: picking pockets, eavesdropping on conversations, performing tasks for fellow assassins, and interrogating informants. In order to find out where you need to go in order to accomplish these tasks, you must climb up to various viewpoints throughout each city. (Though how you learn where to eavesdrop by simply climbing up a building is beyond me.) Regardless, turning Altaïr into a medieval Spider-Man in order to reach high points is one of the best parts about the game.
Beware of a slight spoiler about the "twist" in the 2nd paragraph of the review.