Greasemonkey is a Mozilla Firefox extension that allows users to install scripts that make on-the-fly changes to specific web pages. As the Greasemonkey scripts are persistent, the changes made to the web pages are executed every time the page is opened, making them effectively permanent for the user running the script.
I am a regular Greasemonkey user and have added lots of Greasemonkey scripts which help me a lot, for instance for Google Reader i use Google Reader Custom Search which adds a search button for feeds, Google Reader Optmized which restores some screen space for me and Google Reader + Bookmarks which allows me to instantly add a bookmark and store it in Google Bookmarks to any article.
Makeuseof.com has a list of 20 must-see Greasemonkey addons which can be used for various improvements for your browsing.
I make use of most of the scripts but found a few new ones there which have begun using.
If you want to use GreaseMonkey you will have to first install the Greasemonkey extension and restart firefox once, once you have done that you can head to userscripts.org and find any scripts that may be useful for you and click on the install script button to install it.