If you want to become a web designer, you will need to learn HTML, CSS, and probably JavaScript. You should also learn how to use a graphics editing application such as The GIMP (free) or Adobe Photoshop (not free).. actually there are quite a few graphics editing applications out there.. I will write a post later about your options here. Now, you don’t have to learn HTML or CSS, but if you want to design/build actual websites, you *will* need to. To become a good web designer, you must learn CSS and have a decent understanding of it.
Just to be clear.. For the process of creating a website, there are usually two sides to it.. The Design side, and the Code side. Therefore, many website projects have a team of people.. but you don’t have to have a team. You can learn both things your self and be your own team!
Let’s make an example for a new website project. There might be a designer who does the initial design/layout of the proposed website, the programmer or coder, will then take that design and turn it into an actual functioning website that you can navigate/browse/mouse-around with.
Designer - Uses a graphics editing application to design elements such as the websites’ look.
Coder - turns that design into a working site using HTML and CSS, and uses maybe some JavaScript (if wanting to get fancy, etc.)
Here are some explanations on these things:
HTML - Hyper Text Markup Language, you use HTML to build websites, all websites use HTML. This is the most basic building block of any website. To learn HTML, go to a good search engine such as Google, and search for “html tutorial”, you should get a billion or so results, don’t panic, just check out the first few pages of results and you will pick up HTML in no time.
CSS - Which stands for Cascading Style Sheet, any real web designer will have decent knowledge of CSS, using CSS you can position/style elements/things on your website with precision.. Seriously, with CSS, if you get that down, you will be better than most of the “web designers” out there churning out table infested websites. Again, go to any decent search engine such as Google, and search for “CSS tutorial”.. Go through a few tutorials, and you will pick up a little CSS, I must warn you, CSS has a very steep learning curve, a lot of people get frustrated with CSS because it takes them hours (maybe tens to a hundred!) to understand the concepts behind it and how it works with HTML.. and how to do some certain thing, even some basic thing that you could easily do with tables.. but yeah, good things take time, and knowing CSS is a great skill for any web designer. So get learning 
JavaScript - If you want to add some user intervention to your website, JavaScript is what you will use. If you want images to preload, or images to change their image when the mouse if hovered over it, you can use JavaScript (you can use CSS too, but that’s not that point). If you want to pop up a message box on the screen when a visitor comes to your website, you can use JavaScript. And again, to learn a bit of JavaScript, go to Google and search “JavaScript tutorial” and check a few results out.
with HTML, CSS and JavaScript, you can build some pretty killer websites, ofcourse you should have designed the site already in the graphics editing application, then you use those 3 “technologies” to build the website.. or web application…
Tip: Web Designer usually desings the website using a graphics program, a Web Coder/Developer usually codes or turns that desigin into a working website. Now, alot of people use those terms interchangeably, or incorrectly.. Go figure.
Graphics Editing Application - You use this type of software to create the actual look of the website, or any thing graphical (duh!) such as buttons, banners, backgrounds, content boxes, advertisements, etc.
That wraps up Part 1 of Web Design Basics.
Take it easy, pace your self, it takes time to become a good web designer. Look out for Part 2, I will actually write a tutorial for designing and coding a website using HTML and CSS