\documentclass{article}
\usepackage{graphicx}
% Title gets counted upon definition, not when
% \maketitle is run, but this will often be OK.
\title{Title words are counted as headers}
\begin{document}
\maketitle
\section{Section titles are also counted as headers}
The main text of the document is counted as words in text and
distinguished from words in headers, captions, and mathematics.
Can write 5\$ to indicate amount without causing confusion.
Inlined formulae like $E=mc^2$ are counted separately. Numbers, like
13, are counted like words, but $13$ is still counted as an inlined
formulae. For displayed formulae, there are several ways of writing
them. The best is probably
\begin{equation}
\sum_{i=1}^\infty \frac{1}{i^2}=\frac{\pi^2}6,
\end{equation}
but I guess some still use
\[e^{\pi i}=-1\]
or even
$$x^2+y^2=z^2.$$
The script does not understand that \ae{}, \o{} and \aa{} are letters
and ignores them, splitting a word like h\o{}ys\aa{}te into three, but
who uses these any more? However, proper encoding allows these letters
written directly, e.g. as høysåte, though they may not display
properly. Check that your special characters are treated correctly!
\begin{figure}
\includegraphics{nicefigure.eps}
\caption{Words in captions are counted separately, and figures and
tables are counted as floats (admittedly a bad choice of name since
this also applies to tables that do not float).}
\end{figure}
I may have forgotten some commands, so please check the output to
ensure that there are no major errors. Colour codes makes this ease:
this does not work in Windows, but one may then output in html format
and open this in a browser.
\end{document}