This is a guide for Windows Vista users who want to use LaTeX, are comfortable with "open source" software, and who want to install good software without spending any money. The goal is to install a system that will help you edit LaTeX markup, and then process it to make complete documents. The proTeXt package described here includes all you need to edit and process LaTeX on a Windows computer.
Go to www.latex-project.org, and click "Getting LaTeX". Follow the recommendation to use the proTeXt package. It's almost a gigabyte in size, so make sure you have a reasonably fast Internet connection. After it downloads, it should begin self-extracting into a directory called proTeXt on your desktop. Open that folder, and double-click the "setup" file, which will launch the Adobe Reader to view the installation instructions. You'll see these are not just instructions, but also an interactive program that guides the installation.
The first program that gets installed MiKTeX, which is the TeX installer. You can run it any time via the Windows menu Start -> All Programs -> MiKTeX 2.8 -> Maintenance -> Settings.
The next program, which is listed as "required", is the TeXnicCenter editor. Even though you may already have an editor (e.g. Vim-LaTeX), go ahead and install TeXnicCenter, and compare the editors. To test it out, you'll need a minimal LaTeX input file, which is:
Mic test: pop, pop, popsicle; ice, ice, icicle; test, test, ...
Ghostscript and GSViewEdit
Ghostscript is a tool for displaying PostScript files on your screen, as well as allowing you to convert PostScript files for a non-PostScript printer. After you install it, you can run it using Start -> All Programs -> Ghostscript.
GSView is the graphical user interface to the Postscript interpreter, Ghostscript. After you install it, you can run it using Start -> Start -> All Programs -> Ghostgum. GSView is "nagware", which means every time you use it, you have to click a button to dismiss the message asking you to pay money to register the software, but there is no requirement to ever do that.