Greasemonkey is a Firefox extension that lets you edit the DOM (ie the page) on the fly after the page is downloaded and parsed, but before it is rendered. Thus making it very easy to tweak pages slightly. For example it could search text for text that starts with
http:// but is not a link, and replace the text with a link to the location. This provides a very powerful way to edit web pages on the fly.
Dive Into Greasemonkey is an excellent guide for greasemonkey. It covers installing it all the way to very complex examples.
In the start most people added their scripts to a Wiki (Dead). This soon exploded with user contributed scripts, hundreds of them. This soon grew very big, fortunately help was at hand and userscripts.org (Dead) was created. It is a much better repository.
I wrote some (UPDATE: now unmaintained) greatemonkey scripts:
DLC (Dead Link Checker) - 28/10/2005 dlc.user.js
IMDBRatingAdj - 03/02/2009 IMDBRatingAdj.user.js