Many Ham Radio operators are interested in PSK-31. You will need some type of sound card interface to go between your radio and computer. Once you have the basic interface working, you are then ready to use many of the other digital modes. JT-65, WSPT, FreeDV, SSTV, Digital SSTV, RTTY and many more.
If this is a little too fast, watch this video too.
http://youtu.be/FmsFhz_dyAg
Tigertronics
http://www.tigertronics.com/
Buxcomm
http://www.buxcomm.com/catalog/
West Mountain Radio
http://www.westmountainradio.com/
Timewave
http://www.timewave.com/
Easy Digi
http://www.ebay.com/sch/cliffordwareham/m.html?item=220896968460&rt=nc&_trksid=p2047675.l2562
Lots of good sound card interface info here-
http://www.qsl.net/wm2u/interface.html