I've been using Fireworks for 3 years now, and
my current site and
latest business site are my best work. This came about by spending many hours playing around with the program. I also learned quite a bit by working in an 'intern-ish' position at a local web design company:
360 Mediaworx. I also use Dreamweaver extensively to construct my sites.
If you can find someone local that has a solid grasp and can work with you, you'll learn a lot faster, as well as things you may never pick up independantly. Also, to get better at the actual graphic design part, look at every cool, well built site you can, and emmulate them. Not rip-off copy, just incorporate their ideas into your own, and let your own ideas naturally blend into your work.
Hope this helps! By the way, stop by
my personal site, especially the website design section for some design ideas to get you started.