I work in this area and will tell you that more and more it is getting into programming rather than HTML.
In the beginning, there was HTML. HTML, in essence, is very simple and can be picked up in a night or two. That will provide you with basics. I suggest getting a SAMS.NET "Teach Yourself HTML in 7 days." You can probably make it through in 1 night. HTML is simple, straight forward, and what much of the internet uses as it's base coat, so to speak.
However, more and more, actual programming principles and methods are being used. It's vital to know programming if you start getting into deep Flash. Flash Actionscripting is fairly similar to Java. Those are somewhat relatives of Visual Basic. So, I would reccomend learning VB and some Java.
Also, most websites now are built on databases which provide dynamic content. Database design is essential in web design now because people expect your site to do alot more than just sit there like a painting.
HTML will get you started. However, HTML is merely a base nowdays. The real work is getting Flash/Databases/PHP/Perl all to interact properly.
Thus, I'd say picking up VB would be a good start. Then, make sure you get into database design and implementation.
This is relavent if you are wanting to create the web pages. Many people are under the assumption that one person designs, codes, and polishes up a website. More and more nowdays, there is a team that designs the site. These people are graphic design folks with degrees in design. They move it on to the programmers once they lay things out. The programmers then do the dirty work like implement the databasing, use Flash to animate what needs it, etc. Basically, the programmer gets whatever the designer planned and is forced to make it work.
You should probably decide which side of the fence you want to be on. Typically, you either layout or program. However, if you can layout a page and know a good amount of programming, then you're more valuable. But, you're probably going to be limited to either/or if you want a good paying job with an established company.