I always thought, given that matter is energy, that people who step into a transporter beam are somehow translated into energy and then "broadcast" like radio waves are broadcast, to the planet or wherever, where they energy was translated back into matter.
I never really figured out how it worked from the planet back to the ship though.
I think the original version of Willy Wonka gave the best explanation of this.
Honestly, with all these good movies and TV shows, I never understood the need for the University degree. Anything anyone needs to know can be pieced together by watching the correct sequences of media. To quote Dr. Brian Oblivion: Television is reality and reality is less than television. So, my advice to the Star Trek geeks: quit over thinking things and just go with it. It's only reality after all.