The telephone works by converting the sound vibrations of your voice into an electrical signal which can travel down a wire. In the telephone transmitter (where you speak), carbon grains compress and relax with the sound vibrations of your voice. Electrical current is running through these grains, and when the grains are compressed, they pass more current. This is the way the sound is converted to an electrical signal.
The electrical signal gets sent down a wire to your local phone company, where it is routed to the phone of the person you're speaking with. When you dialed the phone number, you gave the phone company the "code" of where to send your call. How is the electrical signal then converted to the sound you hear? Well, in the phone receiver is a small speaker. The electrical current moves through an electromagnet which vibrates a metal membrane and creates the sound you hear.
If you are making a long distance call, the electrical signal from your phone is converted to pulses of light which travel down optical fibers.
How are they able to put lots of conversations on the same wire (or optical fiber)? They do it by a method called multiplexing (what a cool word!) First, the electrical signal from each conversation is converted to a series of digital pulses. The pulsed signals from several conversations are then mixed together and sent down the wire. At the receiving phone station, the jumble of pulses is decoded and converted back into electrical currents which are sent to the right phones. This process happens so fast that you don't even realize it is happening!
Much research here at the University of Michigan and the Ultrafast Optical Science Center is done on how to make telecommunications betterby making faster lasers and light detectors, and better optical fibers. When you are touring a lab, ask if any research being done there is related to telecommunications!