TeX and LaTeX are more than twenty years old. They were released as free software. Over the years, users have created add-ons to TeX and LaTeX, so that the actual programs TeX and LaTeX are now a small part of what you actually need. Consequently, you actually download a "distribution," which contains TeX and LaTeX, and an assortment of other programs.
Users who are just beginning with TeX and LaTeX aren't really in a position to judge the relative merits of the many available distributions, so the approach here is to suggest a single distribution per operating system.
Windows
For Windows, download MikTeX.
Mac
For Mac OS X download MacTeX.
Linux
For KDE try Kile.