I learned how to do website devel by just doing it.
Age 14-16 I did my own website, some stuff for friends, etc. and also worked for a nonprofit who was just getting off the ground. That was enough to get my feet wet and build a pitiful little resume (which I was quite proud of).
When I got to college that pitiful little resume scored me a position on the school's webteam. That's where I really learned my stuff. It was an ideal setting. As a student developer I was very much in an apprenticeship-style setting. At first I was given small tasks and gradually, task by task, the senior developers taught me new concepts and programming techniques. The school's parameters for the visual design of the website were just loose enough that I had room to grow and experiment, yet they provided the guidance I needed as a novice. After a year of working there I had gone from just basic HTML knowledge & limited experience with graphics to being able to write in ColdFusion and manipulate Oracle databases and wield Photoshop like a pro.
Recently my boss there decided he didn't want to do any side work anymore and gave me all of his freelance clients. In addition to those, I had made contacts with many of the faculty and staff at school and scored some contracts from them. The money I made with freelance fast eclipsed my pithy student wage, so I was able to quit my job.
I've got 12 clients right now, their websites in various stages of design, redesign, and completion. I make between $200-500 a month from it--not huge money by any stretch of the imagination. However, as a student my needs at this point are fairly minimal, so it works. It's somewhat unreliable, as well--i can go almost a month without hearing from anyone, then the next month it seems that everyone wants something at the same time.