That statement is somewhat incorrect. Tables are essential when developing HTML emails that WILL form part of most web designers work schedule.
Sure, learn divs and css - specifically start looking at css 3 and it's uses, but unless you want to be a hardcore front end dev then purely a knowledge of how it works is sufficient.
You'll find that most digital studios will have designers, front end dev's and then the geeks. It pays to know a little of each, but unless you're going to be a freelance one man band then i'd focus my energies on one skill.
This, but tables should never be used for layout, as this is not what they were made for.
When you say web design, there are so many elements to it - design concepts, mockups, implementation of the design into a CMS or coding, developing the site. Which bit are you aiming to get into?
I use Dreamweaver at work but seeing as i never venture into design mode or use it for anything except coding / FTPing, i feel it is very bloated and I swear the stability of it is getting worse, version by version. CS5 is constantly crashing on me. At home I use Coda, which does exactly what I need it to. It also has a lot of features that Dreamweaver has, but it is a lot less bloated and nicer to work with in my opinion.
I teach myself exactly how Jon.G said - Do what I can, Google any bits I get stuck on or need a hand with, find tutorials, forums and examples etc, then develop from there.
W3S has been found to be incorrect in many places, so i wouldn't solely rely on that for your learning it from scratch, just a heads up.
the videos over on css-tricks.com have been invaluable to me (and the website as a whole tbh!) -
http://css-tricks.com/video-screencasts/100-lets-write-semantic-markup/ watch that for a starter in HTML5 and it should put you on the right tracks (I think!).
^
Thats a lot or ramble tbf, if you got any questions fire them in here, there are plenty of web designers like me on here who will give you a hand, I'm sure.
