Just thought I would add my two cents in here. I think one of the greatest things about web design is that there are just so many options available. You really just have to decide to start somewhere and learn the rest when you need to.
Figuring out where to start is usually the hard part. One of the places I recommend is http://www.w3schools.com/ this site will help you begin to get a grasp on some of the many aspects of web design.
It was said above that some of the best web sites are created with some sort of interface or program. I never like to give blanket statements such as this, but that is a fairly good assumption. An interface does not necessarily mean that it is a WYSIWYG (What You See Is What You Get), it could be something that simply helps format and color your text based on what type of file you are creating. Something like notepad++ is a great program for that. I am still creating the code from scratch, but it is easier because the text is formatted and colored for me to easily edit it and ultimately write it.
When you get beyond a simple site (static and a couple of pages), it is sometimes a better idea to use something that will help you with the type of job you are doing. This is where dream weaver and even MS Visual Studio can start to come in handy. This is something you can get into later. The MS Visual Studio express editions are available for free and so is notepad++. Visual Studio web developer is a great interface to use for writing html pages. I have started to use it more and more lately.
I think one of the best ways to learn is to probably design the page in a program such as photoshop. Most websites are designed in such a manner. Then slice the image up and write the html and css to make the page look like the design you created in photoshop. There are many tutorials on how to do this. Just use google to look them up. You will be surprised at how much of the page you create using just html and css and how few images you will use, once you get better. You want to use fewer images to help with file size so the page loads faster. Using VS web developer you can also create master pages which is basically a template. So you create the first page as a master page and designate your editable regions. Then when you create additional pages based off your master page, you need only create the editable region and the rest of the page (navigation, menus, header, footer, etc) are already there. Makes building additional pages very easy. Dreamweaver has this ability as well, using templates. The best thing about master pages/templates is that when you want to change them it will filter the change to all of the pages that were created using them. This comes in handy when you need to change a menu item on 150 web pages. Could you imagine doing that by hand? Yuck!
That is just some of the reasons why programs to help you build your pages can be quite useful. You just need to find the right tool for the right job. If you are really serious about web design I would start with photoshop. I know that sounds weird, but I use photoshop more than I use most any other program when I am designing a web site. My clients sometimes even ask for the psd file (photoshop file) so they can edit the images later if needed.
Remember that every designer started where you are at right now. Some of us did not have many of the options that are available today. So take advantage of that, and you will learn much faster.
If you have any other questions, please feel free to ask.