My words aren't being hyphenated

Let's assume you've selected the right TeX 'language' - as explained in "how hyphenation works", you're not likely to get the correct results typesetting one language using the hyphenation rules of another. (Select the proper language, using babel if you're a LaTeX user. This may reveal that you need another set of hyphenation patterns; see "using a new language" for advice on how to install it.)

So what else can go wrong?

The \hyphenation command allows you to give explicit instructions. Provided that the word will hyphenate at all (that is, it is not prevented from hyphenating by any of the other restrictions above), the command will override anything the hyphenation patterns might dictate. The command takes one or more hyphenated words as argument - \hyphenation{ana-lysis pot-able}; note that (as here, for analysis) you can use the command to overrule TeX's choice of hyphenation (ana-lysis is the British etymological hyphenation; some feel the American hyphenation feels 'unfortunate'...).
hyphenat.sty
macros/latex/contrib/hyphenat (zip, browse)

This question on the Web: http://www.tex.ac.uk/cgi-bin/texfaq2html?label=nohyph