In 1958, the Department of Defense launched the first communications satellite: Score.  It was an active satellite in that it had its own equipment for receiving and transmitting signals (as opposed to the passive satellites, see below).  Score had an onboard tape recorder, which was used to record the signals that it received and then retransmitted the signals to the receiving stations as the satellite passed over the stations.
In 1960, NASA launched its passive satellite: ECHO 1.  It served to only reflect signals that were sent up to it towards their destination.  The satellite was an aluminized plastic balloon that was 100 feet in diameter.  The usage of this satellite was very limited due to its nature; the transmitters that sent the signals had to be very powerful and the receiving antennas were large.
Today there are hundreds of active communications satellites circling the globe.  Their methods of transmitting signals are much more complex now, having to amplify the signals received and transmit them at different frequencies to their destinations around the world. (see also Artificial Satellite.)