If you're building a site from scratch with no templating system, and even if you are, the minimum you need is a good text editor. On PC I would recommend Notepad++; on Mac, TextMate. When I applied for my last Job, I mentioned that I used Dreamweaver, which I did at the time, and they simply laughed at me.
That being said, Dreamweaver is a very good tool. If you have it, use it, but don't feel that you need it in order to make good websites.
I would sooner explore JavaScript and the JQuery library than look into Flash. Unless you are a Flash guru, I think it just makes a website look cheaper and, more importantly, less usable. For one, on Derrek Lau's website, you can't copy/paste any of the text, nor search through it. Nor bookmark individual pages. As it happens, JavaScript and Flash's ActionScript are almost identical.
The way a lot of professional sites work is through a content management system and PHP, as DaveV said. If you're starting out, such a route can be a little daunting. There are web hosting companies (I can't name any off the top of my head) that give you the option to work solely with templates ("No HTML required") and this is essentially a content management system, albeit set up by them rather than you, and in some ways rather limiting, but it's a start, and doesn't require you to know PHP. Provided that they also give you the option to "edit the CSS", you'll be able to customise the template and make it look like almost anything you want it to. CSS is difficult but it's an integral part of all modern websites.
If you set up your own CMS, it will require you to set up a database, which can also be daunting. There's one tool I came across called Stacey (staceyapp.com) that doesn't need it: you just make a bunch of folders on your computer, call them whatever you want your pages to be called and structure them how you wish, inside each folder you make a text file, which will probably look a little like this:
Code:
Welcome to My Website
=====================
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
Here's a link to [some other page](http://www.example.com) and an picture of .
* Here's a list item
* and another
A Sub-Heading
-------------
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
Rather neat, no-nonsense. You then upload all these folders to your website and you're ready to go. Once again, the skill you'll need the most of is CSS, as well as some HTML and getting to grips with some proprietary templating code, and possibly some PHP. It's more complicated than the other route, but you have more control.
That's basically one small step down from what DaveV was suggesting. I swear by Stacey for small, content-based sites; it's not as good for highly interactive, application-based sites, though.