Steps you will need to take to become a website design:

1. Your first step at becoming a web designer is to learn Photoshop. Using Photoshop, one can create logos and website designs they can sell to Web Developers. One can also get a reality check to whether they have any design skills or not. You can download a free 30 day trial of the latest Photoshop software from Adobe's website. Refer to YouTube.com for Photoshop tutorial videos.
2. Tinker with HTML and CSS. A good place to start learning CSS and HTML is W3Schools.com, they have all the tutorials you'll need. It's a language that you can become fluent in with enough practice. A good coder isn't one to memorizes all the code, but is good at referencing and implementing it. Also Photoshop has a 'splice' feature for web designers. Photoshop's splice feature allows you to save your website images into smaller pieces so you can more easily turn your website image into an actual web page. To make editing and managing web pages easier you're going to need a HTML editing software or website editing software. All website developers and designers use editing or authoring software. Go to Adobe's product download section and download the 30 day free trial of  Dreamweaver.
3. Once you've got a good understanding of HTML and CSS you should make it a point to learn JavaScript. This is the extent of web design and is actually crossing the boundary into Web Development slightly. Websites are almost all interactive these days and this mean JavaScript will almost always be used.
4. It's time to learn Flash. Steve Jobs(Apple) would like to turn a cold shoulder to Adobe Flash because it's powerful presence in websites rival smart phone apps. Despite Apples dislike of competition... Flash isn't going anywhere. Sense you've learned JavaScript, understanding the code used in flash (ActionScript) will be much easier. ActionScript is the code used in coplex Flash website applications and is almost identical to JavaScript. To start learning Adobe Flash go to Adobe's website product download page and install their free trial for 30 days.
5. You can make a living if you learn the languages and software listed above. You will be a web designer. You will still be dependent on web developers to finish your websites for any back-end functionality. If you want to be self sufficient and able to create website's from start to finish on your own you will need to become a Web Developer also.

Don't under estimate YouTube.com for Web Designer related tutorials. Web Design is a highly competitive field and you will be competing world wide.