For Mac OS X, MacTeX is the de facto standard. You can download the distribution package here: https://www.tug.org/mactex/
This will install a number of things in your /Applications/TeX folder, including a text editor called TeXShop, and a package manager called TeX Live Utility. First, we'll get your packages up to date.
Open TeX Live Utility (/Applications/TeX/TeX Live Utility.app) and let it analyze what packages you have and what updates are available. Once it displays a list of packages, navigate in the menus to Actions > Update All Packages. Once it's done, you can quit TeX Live Utility.
For Windows, Tyler recommend using the MiKTeX distribution of LaTeX. To install, follow the directions below or directly from the MiKTeX website:
Once you've done that, you should have a working LaTeX installation. MiKTeX comes with a text editor that makes typesetting LaTeX documents super easy.