I agree with DennisChang. I have been in web design for almost 12 years and have never had someone ask me about my educational background. They ALWAYS check out my portolio, however, and most of my business comes from word-of-mouth recommendations. I am self-taught, but that is the way I learn best.
As far as learning goes, thank God you want to!!! There are far too many "web designers" that simply purchase editing software and go into business. At the very least you need to have a thorough knowledge of html and css or you won't know how to problem solve or clean up the sloppy code generated by ALL html editors. You also need to have an understanding of organic SEO, design layout, typography and the various aspects of webhosting (setting up email dns, installation of scripts, forms, etc.)
Don't start with outdated software. You will outgrow it quickly and then have to re-learn a whole new program. It's hard to keep up with what is best because something new always comes along to trump it, but Dreamweaver is a good choice. It's what I use and is very popular so you can find lots of info and tutorials online.
Good luck with your adventure!
