Forget dreamweaver. It's an expensive crutch for people who don't want to dig in and figure out how stuff really works. It's not a bad program, it's just that if you want to really learn, you need to get your hands dirty.
Find yourself a good text editor and get to it. Price should range from free to maybe 100 bucks. On the mac side, I like Textmate, which is about 30 bucks, I think, and worth every penny. Don't know about windows, but just try some out. Many are free, and almost all come with a free demo. Try to get one that handles CSS well to (with syntax highlighting and stuff). It will make your life a lot easier.
For multimedia stuff, bite the bullet and get Flash, and a good book. I don't do much of that stuff myself, but you can do a lot of really cool stuff, if you're so inclined. You may want to come back to flash later, though. It ain't cheap either.
Now, for learning, way back when I learned, we all just viewed source and figured out what other people were doing. You can still do that, but it's a lot harder than it used to be.
Be wary of online tutorials. Lots are out of date. If it mentions standards-compliance, that's a good sign. If it starts talking about creating a bunch of tables, that's a bad sign.
I've heard good things about this book: http://www.cookwood.com/html6ed/ so you may want to pick that up.
As gameboy said, w3schools can teach you a lot. the w3c web site (http://www.w3.org/) can teach you EVERYTHING, if you can understand what they're saying.
Get yourself Firefox and the web developer toolbar extension. It's indispensible.
Start hanging around sites like alistapart and smashingmagazine.com, and you'll be a thick glasses-wearing, turtleneck sportin' nerd in no time.