Buy the related literature first and give it a read through. HTML for dummies won't run you much, then you can move onto more in depth books and implement other languages.
Web design IS one of the things you can become proficient in at home without training then get yourself onto a course and get qualified.
You can't really make a career on web design though, I don't know any real 'web designers' that do web design alone, the trend these days in companies are the so called 'front-end developers' - people that take care of the design while at the same time make sure client interaction works and information is displayed in an intuitive way, a front-end developer should be specialized in various javascript libraries such as jquery, knockout.js, etc... they basically plug the back-end with the front-end.
Problems a web designer/front-end developer face in the modern economy: are they REALLY needed? I'd love if companies employed these people full time, but it's simply not profitable... when a project manager see's a programmer/developer with a knack for design, that guy is probably going to get all the work (and be paid accordingly - I hope ), unless the project is truly big (in profit terms), companies don't see a point in assigning design specific people.
Web design, like any sort of 'x design' is an extremely competitive market, the people that triumph in the design world are the best at what they do, there isn't much room for others.
And I'm rambling again.
Anyway, I work as a web developer in the financial industry, previous to this I did some cryptography work (a lot of my work goes into web security). Although most of what I do is code heavy, I can also dwell into design (HTML5/CSS3).
My dream is to one day cash out, buy a boat and travel the seas like a big gay sailor.