LaTeX is a macro package for DonaldKnuth's TeX typesetting language. See http://www.latex-project.org/ for more information.

Someone want to write some sample LaTeX files here and how they compiled.

Rather than specifying the exact layout of a document, for example fiddling with fonts and margins in a WYSIWIG word processor such as MSWord, you specify the structure of the document. (A bit like what HTML was supposed to be like before the internet became commercialised. :)) It offers much greater control over layout and appearance than other word processors.

Basically, people a lot smarter than you have come up with good formatting guidelines for different document types, so you don't have to worry about that sort of stuff. You just write something like

\section{Section Heading} In a technical report, you should always have some text between a heading and a sub heading, so here is a sentence.

\subsection{First Subsection} Blah blah blah...

LaTeX automatically keeps track of section and figure numbers, and comes with packages to help keep track of bibliographies/references. Source files get processed and can be converted into popular formats such as PostScript and PDF.

LyX is a WYSIWYG LaTeX editor, or something approximating it.

Also see the man page, latex(1)

To learn how to compile documents with Latex, see LatexMakefiles.

I'm not a LaTeX Guru?. Could someone give a complete LaTeX example, of perhaps how you'd write up a small article about the wiki, and how to build it, and how to display/print it. I'll put up a PNG of the output that we can link here so people can look at it.

(The correct spelling is LaΤεχ, but it is neither a WikiWord, or easy to type.)