First Principles
Unlike many document creation programs used today, (La)TeX focuses first and foremost on document structure. As a result of this mind-set, most often TeX is written much like a computer program rather than like writing a document in the common office suites of the day. This means that you want to select an editor to edit the TeX "source code" you will write and a TeX engine to process this to produce the output typeset documents.
Editors
A common editor to use in a windows environment is WinEdt. Another option for an editor WinShell.
TeX Engines
MiKTeX is the most common TeX engine for the windows environment. A friendly install page is here.
TeTeX is the most common TeX engine for UNIX environments. However, before you grow frantic about installation, it is virtually certain that it is already installed in an academic environment.