These scripts can be almost as powerful as add-ons, and they're usually just as easy to install. Find something you like at Greasy Fork, click the link to read more, and if you like the sound of it, click "Install this script". A warning dialog explains what you're about to do, so there's no risk of silent installations. There's an option to view the script source, but otherwise you can install it with a click. Installed scripts can then be accessed via an extra tab on the Addons page, where you'll find buttons to set options, disable or remove them.
Greasemonkey also provides simple tools to create and manage your own scripts (click the Greasemonkey button on the address bar and choose "New User Script"). Even experts may find it a challenge to get everything working, but fortunately Greasemonkey has a comprehensive wiki to offer help and advice.
Version 3.9 changes (News):
Improve the performance of GM_getValue/GM_setValue. (#2197, #2025)
Add a rich tooltip to the Greasemonkey toolbar button. (#2377, #2418)
GM_getResourceText supports a second (responseType) parameter, for better compatibility with binary files. (#2376)
Global exclude rules no longer require a Firefox restart to take effect. (#2410)
A web page whose url ends in ".user.js" could fail to load. (#2407)
A script whose name ends in ".db" could fail. (#2402)