I started college in 1995, the same fall that Netscape came out. A friend of mine showed me how to create a piece of HTML code, FTP it into the public_html folder of my unix account, and then I had a "home page". The unix accounts were set up by the college... anybody else remember reading e-mail with Pine? I would never have figured out hosting and configuring a web server on my own.
We learned how to code web pages as the features were being added one-by-one: tables, frames, animated GIFs, java applets (embedding them, not coding them). I was not a CS or programming major, this was just my hobby.
In the summer after sophomore year, I started making money at it by building static web pages for businesses in my home town. It's a small town and I can honestly say I was the first web developer there. I don't remember how I advertised myself... maybe people just contacted me because they knew my parents or something. The biggest source of business I found was the real estate agents, who wanted a different page for each house they were listing, and frequently updated them. For me it was pretty simple to copy the template and update the navigation (remember, all hard-coded, even the "prev" and "next" buttons), and I would charge $50 or so for each new listing.
In my senior year I did an internship which became a paying job, still doing HTML "integration" as they called it. In my second job, a year later, I learned about dynamic pages, CGI, databases, and ASP. I had a great boss who was an entrepreneur with lots of ideas, and he hired me to sit in the office next to his and try to find out which ones were feasible.
In particular I remember trying to solve the problem of building an online "shopping cart". First I did it with Javascript and used a hidden frame to hold the data in the browser as the user navigated from page to page. Then I learned Perl so I could code it as a CGI script that stored the data in some kind of a flat file. Then I learned databases (including how to set up and administer a SQL Server database) because I had a hunch that a scripting language like ASP would be the answer. Every time I told the boss I wanted to go to the bookstore and get another O'Reilly title, he would fund it. Fantastic experience, but I left (why else?) because somebody else offered me more money to do HTML tweaking and Photoshop image-slicing drudgery 40 hours a week.
It took me thirteen years to get another great job like that.