To walk and run, the Wii demo used the Nunchuk thumbstick to move around and the Wiimote to change directions. The motion controls are the big showcase with a wide variety of uses besides movement. The main use aside from moving is the flashlight. Holding it just like a regular flashlight, even shaking it when the light starts to flicker to get it back on. All portable light sources use the Wiimote, including flares. Your enemies hate light, so you can use it to drive them off to a certain degree.
The motion control draws you further in to the survival horror experience by how you use it to interact with the environment. To open a drawer you use the Wiimote bottoms to grab the handle, and pull back on the controller to open the drawer. This is the same for doors and objects you need to move and control for environmental puzzles. Even enemy attacks take advantage of the controllers as you need to jerk and swing the controller to shove them away or throw them off.
One of the coolest (and freakiest) of the Wiimote features is when you receive a one-way phone call from a cell phone you find in the game (replacing the walkie-talkie from the original). The audio from the other line comes through on the Wiimote speaker, so you hold it up to your ear to hear the call.