The demo starts you out in a port town, unarmed, with a directive from your fairy friend to go talk to your grandpa. After a visit to Grandpa, you head out to a monster-infested area, then your general jaunt around town (Go talk to this character! Go try to cross this bridge! Oh, the bridge has collapsed! We should talk to Grandpa! etc.) The demo spent just enough time not giving you the sword that I was starting to get a little antsy; however, one final visit to Grandpa got me my weapon, and he then went about teaching me how to use it.
It's as simple as can be: tap enemies to attack, draw a line to do a sideways slash, draw a circle to do a spin move. With this equipment and knowledge, I was allowed into the northern part of the town to fight some ChuChus as I made my way into a cave and some puzzles. The first puzzle asked me to write on a sign the number of palm trees on the beach (spoiler: 7) before I was allowed access into the next room. The rest of the rooms followed a similar pattern: a few enemies, a few puzzles that involved doing things in the right order, and key-collecting. Very Zelda.
But, as standardly Zelda as it sounds, I must stress this fact-- I can't remember the last time I had so much fun just making a character walk in a game. Directing Link around with the stylus is a lot like movement in Animal Crossing, but faster; it turns out, the speed makes all the difference. Simple activities like pushing and pulling blocks and doing basic attacks are not only novel, but are enjoyable independent of their novelty. And while the controls aren't based on simulating real motions as they tend to be in Twilight Princess (because swinging a sword is rarely like drawing a line), they are much more intuitive and much more natural. If you've become tired of the Zelda formula, or if you just like action-adventure games, or games, consider Zelda: Phantom Hourglass. It manages to be instantly familiar as Zelda while being startlingly fresh.