-As you may already figured out a analog modem communicates with a series of screeches and noise. This is refereed to modulate-demodulate, which is all the noise of digital bits being turned into analog sounds. Your modem has to go between the digital world of your PC and then turn the digital information to a sound which is interpreted by another computer. Your modem has to take digital 0's and 1's and turn into tones and sound. Pretty neat stuff that the modem has to work so hard and still does fairly decent. This isn't the end though, there is much to just screeching and yelling to each other in order to move bits of information.
-For the modem to send bits of digital information in the form of 0's and 1's we need something called frequency key shifting. This is sent in wave form audio format. Now in order to get more information in and out we need to use a more modern method than just frequency key shifting thus came phase key modulation. Key phase came in and added timing delays and to designate a 0 or a 1. This allowed modems to make the transition to 9600 baud. Now in order to do even more we will add volume along with the mix. So now we have a modem that sends sounds in pitch, volume and even delay timing. Now with modems that do this we really need some way of making it standard. See ITU standards.
-Now you have a basic idea of how the modem works lets look at the 56k more. Most of us have upgraded to this at one time beast! I still cant believe people referring to this as a speed demon!? But if you have ever used a 9600 baud modem you can kind of see the were the speed has improved immensely.