MacTeX - free, self-contained package for using TeX markup on OS X Macs, containing a version of TeX and the TeXStudio editor.
TeX for Windows:
MiKTeX - free TeX version for Windows. This package contains the TeX markup language along with its command line editor.
Overleaf / ShareLaTeX is a freemium (some services for free, some services with a subscription) way to collaborate on and share LaTeX documents.
ProTeXt - a self-extracting package for Windows containing the MiKTeX version of TeX, the TeXStudio editor, and Texmaker, a LaTeX editor. This is a HUGE (~2GB) download. Please have patience. It may take up to 1 hour on the fast college network. On Windows computers, you may also need Ghostscript and Ghostview (for postscript) and/or Acrobat Reader (for PDF) to preview your finished TeX documents.
WYSIWYG Editor for TeX - Texmaker is a free, cross-platform LaTeX editor that allows you to see both your markup and compiled document side-by-side for editing and debugging. Versions are available for Mac OS, Windows, and Linux.
Learning Resources for TeX
This series of tutorials on YouTube is an excellent way to learn to create LaTex documents with Texmaker.
Library Guide from Wayne State U. containing a variety of TeX resources, including reasons for using, comparisons with Word, download sites for various TeX editions, and learning resources.