The version of MiKTeX installed in Hayes 025 is a bit out of date now, I think it is MiKTeX 2.4. Even so, if you download and install the LaTeX Editor (LEd), it will find this installation of MiKTeX and use it. That is the easiest thing to do.
The rest of this page describes how to use MiKTeX 2.4 to work directly with .tex files, rather than using a LaTeX front-end. These instructions might be helpful if you are having trouble getting latex to use the right paper size when producing a .pdf file, or if you need to find yap.exe.
Open a .tex file from your flash drive or by saving one from the Math 592 website. The PC's in Hayes 025 do not have any associations with .tex files, so double clicking one will not even open an editor window. You can associate .tex files with WordPad by right clicking, and saying Open, then Open With, and selecting WordPad from the list. When you're ready to process it with LaTeX, you need to tell the computer which program to run, because .tex files are not automatically associated with MiKTeX in Hayes 025. Right clilck the .tex file and choose Open or Open With to get a window like this one.

latex is not on the list, so click Browse, then browse to C:\texmf\miktex\bin and find latex.exe. Select it an click Open.

This takes you back to the Open With dialog box. Here, be sure to check the checkbox saying "Always use the selected program to open this kind of file". This way, when you double click a .tex file, it will be processed by latex.exe.

Running latex will produce a .dvi file. The dvi previewer YAP is already associated with .dvi files, so there is nothing more you need to do. So you know, yap.exe is also found in C:\texmf\miktex\bin.
To convert a LaTeX document to a .pdf file, there are two methods. You can right click a .tex file and add an association to C:\texmf\miktex\bin\pdflatex.exe, as we did above for latex.exe. Or, you can right click the .dvi file and add an association to C:\texmf\miktex\bin\dvipdfm.exe, which converts .dvi files to .pdf. At first, there is no big difference between them, but when you are including graphics, there is a difference. pdflatex must be used when you include .pdf files as graphics, whereas dvipdfm must be used when including .eps graphics files, at least as far as I can tell.
The easiest way to get the right paper size is to use the line
\usepackage{hyperref}
in your .tex source file, before the \begin{document} line. This communicates the letter size you specify in the \documentclass[letterpaper] line to pdflatex.
Unfortunately, the default paper size for dvipdfm is A4, the European standard. To make letter size paper the default, download this file and save it in C:\texmf\dvipdfm\config with filename config.
