Well, I don't know what you mean by professional and what other work experience you have. In my opinion here are 2 parts to this question - one is "how to be a graphic designer?" and the second is "how to be a web designer?" In my experience - the first one is harder to lean then the other.
The web part of this is really technical, I didn't know anything about web design 6 months ago, I got a couple of books and "dreamweaver" and leared how to build simple sites (one that just involved HTML code and don't have other components to them).
As for style - I've learn graphic design for 4 years in a design school. I think it was a too long program, but it did change the way I look at things and solve problems. There are a lot of school that teach web design or graphic design. I think it's also work for some people to just look on a lot of sites and books and see what they like and why, personally, I don't think I could learn it without teachers and other students.
I guess it all depends on what kind of things you are good at and what ways you are comfortable learning anything else.
Methods I can think of are:
1. Go to web design school or take a few courses.
2. buy programs and a book and teach yourself.
3. Get a privet teacher to give you classes
4. if you are more technically oriented, you can research online and just learn to code HTML \ XHTML on your own, without using dreamweaver or other programs.
I guess each method is better for different people.
good luck!