Hi,
Well its going to take a loooooooooooooooooong time to fully educate you on Short Wave radio

However, I would suggest reading this link first to get a general idea of radio.
http://en.wikipedia.org/wiki/Shortwave
Theres many many different areas of Shortwave as you will seen listed in the link. The two basic areas I would say are listening to shortwave broadcast stations from around the world or communicating with shortwave radio operators from around the world. Also known as SHortwave Listeners (SWL) or Amateur Radio Operators (HAMS)
I myself am an Amateur Radio Operator and got my start listening to the shortwave bands. I now communicate with people all over the world in a variety of different methods (voice, mose code, radio teletype, satellite, television, etc) and have a blast meeting people plus learning a bunch about world Grography, Geology, Cultures, Politics, Time Zones, Signal Propagation at different times of day and different seasons, Electronics, Computers, Solar Cycle and how the sun effects radio waves, etc. I also enjoy listening to standard broadcast stations and music to get a different perspective on the world.
Anyways, theres many simple shortwave radios that will receive stuff from all around the world. In most cases, to actually talk or communicate you will require a license to do so (except for CB which is, well, like having an old single frequency radio that gets only one station compared to XM)
Heres a link to some good radios
http://www.universal-radio.com/
If your interested in the Amateur Radio side, I suggest you look at this link
http://www.hello-radio.org/whatis.html
Heres a link to my radio station
http://home.roadrunner.com/~c.constantine/index.htm
http://home.roadrunner.com/~c.constantine/station.htm
Let me know if I can help anymore
