How does an optical fiber work?

When you pick up the phone and call mom or your brother across the country, how is the information getting back and forth? These days, much of our telecommunications is done via optical fibers criss-crossing the country and the world. But how does the light get through the fiber without escaping?

Do you remember when we shined a laser beam through the water tank, onto the lower surface of the water? What happened to the laser beam when it hit the water/air interface? Did any of the laser get reflected back into the water?