The G2 has a couple of user interfaces, though only one of them (top) can be used in conjunction with the LCD display (the other, on the next slide, works with the EVF). Like most cameras, the Q.Menu button lets you navigate around the edges of the display to change settings (middle). This works via touch as well.
While the touch-screen operation is pretty well-done, there's one infuriating, frustrating flaw. If you're in single-area AF mode and you touch the screen when it's not clear that you're going for one of the settings, the camera assumes you want to change your focus area and drops you into that interface (bottom), plus it moves the focus area to wherever you touched. You never realize how often you accidentally hit the screen until you've used this camera for an afternoon.