I just looked through the book, and it's a bit outdated (as it says on the page you're linking to).
Some updated basics:
- Extra possibilities include saving information (though this can be done through localStorage these days) and doing cross-site URL requests.
- Small bits of code (for finding a certain element or doing some basic operations) are best to check through the firebug console.
- Best way to debug: actually install the script in chrome, and use the Chrome debugger to set breakpoints and check certain objects.
- second-best way: Install/use firebug in firefox, and use its logger through unsafeWindow.console.log(element). This will show the element/object in the firebug console, which can be used to inspect further.
Unfortunately the debugger in Firebug doesn't work for greasemonkey scripts at the moment.
- The main difference between firefox and chrome scripts: Chrome doesn't allow the script to interfere with scripts on the page in any way.
Greasemonkey does (mainly through unsafewindow), but that is thought to be a bad practice. Chrome also doesn't allow cross-site URL requests, though there are ways around that.