Since there were so many requests for answers to this question, here is a start toward answering. Please understand the next paragraph as a serious comment, humor intended.
Your question is so big that I do not think most of us ( who, like you, are busy more than all day long) can do justice to it. In a sense, answering how students use the Internet is like trying to tell how students use pencils, calculators, books and chairs.
The Internet has been an essential part of math education in my classrooms for years. The advent of the WWW and browsers such as Netscape make it easy for student to do valuable work. Please try our homepage at the URL last in my sig.file.
Today students have worked on learning UNIX commands, used email, shared Mathematica files, browsed for support materials for projects and played a golf game (to be honest, not all uses seem perfectly curricular ... math is not made by work alone).
Over time students do some pretty good research over The Internet. The University of Washington (local to us) provides some nice resources with "uwin" and students can follow e-research with in person work, in library work or whatever. Swarthmore provides some excellent services through the Geometry Forum. Although my students are irregular in communicating their investigations back to the Forum, they regularly enjoy the Problems of the Week.
Students use Internet services to investigate further education, make e-visits to colleges, plan their finances, and discuss the relative values of various avenues to education.
<<<<<<<<<<<<<<<<<<<<---------------->>>>>>>>>>>>>>>>> from Steven S. Means email@example.com Math and Technology Teacher at Sammamish High School http://belnet.bellevue.k12.wa.us/sammamish/ <<<<<<<<<<<<<<<<<<<<---------------->>>>>>>>>>>>>>>>>