He laid out a very concrete guide to follow for someone starting with an art background, talent for composition, proficiency with photoshop, and a willingness to learn. I'm putting it up as a blog in case other people have suggestions, corrections, or can benefit from the advice. Here is the guide.
- Design your own website in Photoshop. What the website is does not matter, but making it look good does. Think up something obvious (for instance a gallery for your artwork), figure out what pages it will have, what they should look like, then make prototypes in Photoshop. If you've got artistic skills and know Photoshop well, this hopefully is fairly easy.
- Build that website in WordPress or another CMS (Content Management System). Now you know what you want the web page to look like, now try to make a web page that looks at it. You'll need to buy hosting, buy a domain, then install your CMS. Now try to make WordPress serve up pages that look like the ones that you have designed. You will encounter a lot of problems. Google searches will often help you find solutions. Browse http://wp.smashingmagazine.com/ for more ideas. And if you need to compromise on your initial design because you can't figure out how to make it work, do so. The goal here is to get something done that looks nice, and not necessarily to perfectly realize your first vision.
- Start freelancing. Once you have demonstrated that you can build an attractive website, you have a skill that people are willing to pay for. Go to https://www.elance.com/ and start offering your skills as a web designer. You should start at the low end of the free-lance market, say around $50/hour. You won't get steady work, but it is a nice side income. And, more importantly, you're building your experience and a portfolio.
- Look for full time work as a web designer. In a few months you should have 6-8 actual websites under your belt, and will have learned a lot more about working with customers. This is a real portfolio to point to during a search for full-time work as a web designer. Depending on luck, opportunities, location, etc, you might land the job you want, or may need to take an intern to full-time route. A reasonable salary in the Los Angeles area to aim for with the full time job is probably around $70K to do design and HTML. That varies widely over time, by geographical market, by company, etc.
- Upgrade your skills. Once you have a job, you've turned skill at composition, knowledge of photoshop, and a willingness to learn into a real career. But you have just begun. There is a lot more to learn. In particular over the next few years you need to improve on the underlying technologies of HTML, CSS, and JS. You should be trying to educate yourself about UX. You need to build a professional network. There is a long ladder to climb, but at least you've got your foot on the bottom rung.
This outline was recommended by one person that I know who became a web designer. It sounded reasonable to me, but I am not a web designer. Starving art students may be surprised at how quickly you go from designing something for yourself to getting paid significant money for your time. That happens because you're solving real problems. Your combination of artistic talents and willingness to tackle new things is worth far more to employers than either is alone.
Please share if you find this helpful, have alternate suggestions, experience, etc.