The Tools I Use
What kind of an awful author would I be if I just sent you out there into this brave new world (or at least half-assed tutorial) without giving you an idea of the types of tools you'll need to get started?
The worst kind.
Ya, rly.
Surprisingly enough though the tools you need to use CSS on your web page were the same tools you needed to use HTML: a solid web browser and a good text editor. Personally, I'm using Firefox 3.0 for Windows with the Web Developer Add-on (which allows you to edit CSS in real-time) and Programmer's Notepad (which handles indentation, shows you matching parentheses and braces, and does some really good code coloring). All three programs are free downloads so don't hesitate.
If you're in Mac OS X or some Linux variant it should be fairly trivial for you to find a decent open-source text editor that supports code coloring. I would recommend sticking with Firefox however. It's likely 80% or more of your visitors will be using Windows and Firefox does a good job of being consistent across multiple platforms.
And whatever you do, for the love of god, make sure you test your pages in Internet Explorer before you start showing them off to other people. Sure, 99% of the web development community hates IE, but about 65% of the internet is still just IE on Windows. You can be reasonably assured that as long as you don't do anything crazy it'll probably work okay in IE7, but if you don't at least check to see how the other more-than-half lives then you're going to frustrate users and for no good reason.