I've been creating web sites since 1995, and I went legit in 1997 with a business license and 'home office' permit from the city (and all of the tax benefits those afford!) My clients are strictly word of mouth, and their fields and web needs vary. I consult, help with registration and hosting, do web-related graphics, convert audio, and of course format the pages (I still code from scratch.)
But web design involves more than simply making a page, which most people can do with Dreamweaver or Microsofts web authoring program (used to be Frontpage.) There's the creative aspect (which is not my forte, but I take direction well when the client tells me what they want), as well as some internet 'theory' about conceptual and actual dos & don'ts of presenting info on the web. For example, use of typefaces (everyone else calls them fonts,) consideration as to how people view the web (resolution & browser dimensions,) and staying behind the curve a bit - not everybody's up-to-speed with the latest plug-ins or apps. Basically, you have to be hip to compatability, so everyone can view the site the way you intend. I first got online in 1993, so growing with the web gives me an overview on this that newer designers don't have.
Example: there's a high-profile site I created and manage, and there are constant efforts by consultants to try and improve the site. What they end up discovering is that the site in fact does exactly what it was intended to do, and does it very well. I'm not offended by these suggestions, it just reinforces that I know more about what I'm doing than they know about what I'm doing. Not everyone has a better idea.
Like any creative/technical skill, there are many possibilities, and some ideas can be over the top... just like with drumming! And similarly, substance over flash always wins.
So hang in there, make sensible recommendations to clients, and good luck!
Bermuda