Starting Out:
I would suggest that you do local work as a freelance designer to build up a small portfolio. Get your name out there and make sure you do the best work you can so that people will recommend you.
As Matt said, if you are not already familiar with server-side scripting, such as PHP, I'd recommend learning this skill as it could prove very valuable. Ideally, it would be good to be fluent in: HTML, XHTML, CSS, PHP, MySQL & Javascript.
You may also find, the deeper you get into the industry, the more and more programs you will need to purchase and learn. The following are a good set: Dreamweaver, Photoshop, Illustrator, Fireworks & Flash.
However, don't be afraid to take every opportunity you can get to learn and perfect your skills of every program you possibly can, same for coding languages really.
Advetising:
Be sure that your name is permanently floating around, you need to constantly advertised. Contrary to popular belief, a good marketing campaign does not, necessarily , mean a $xxx,xxx budget!
Make some flyers on your home computer, print them off and put them up. Do the same for business cards to, and maybe even expand into other areas of promotional items (marketing is all about imagination

). It might be worth getting the items printed out by a professonial printing company such as Vistaprint, there are many others too.
Using Your Experience:
Now, once you have done this for a while, you should have quite a large customer base, and it is then time to either approach a local design company, or, you may feel you are doing well enough to proceed into full-time web design for yourself as your own company.
Now, when you go to a company, you can say "I have done work for x, y and z clients and they were all very satisfied with the work I produced." If you could testimonials from your clients then that would be even better or maybe even provide a contact number (with the company's permission, of course) so that your prospective workplace can, perhaps, call up the client and ask what they thought of you (just make sure you
did make a good impression

).
I'd take the "own company" route myself as I feel it leaves more room for expansion and is a more versatile route which offers more opportunity, but, heck, don't listen to me, I'm just a 15-year old kid, right

?
Conclusion:
Anyway, do not think that progressing in web design as a profession is an easy ride and you'll be making millions in a year - you won't. I'm not saying that it is not
possible to make millions, but it will take years of dedication and hard work and either a job as a Senior Designer at a large company or a succeeding business.
Good luck, and I hope you do well. In this industry, I find that it is more about experience, than education. Also, bear in mind that in the outset, it will be tough, but, if you have a true flair for design, then you will be prepared for the long-haul. Hope I helped you, any more questions, feel free to ask, should you feel the need!
Thanks,
Will.