Web design and development are nebulous, but lucrative, fields of employment. In many ways, they are exemplary of the opportunity-driven, Wild West mentality of the internet as it stands today. The tool-set to start your journey is incredibly accessible, meaning that anyone around the world can try their hand at whatever part of the industry intrigues them the most. However, because of the subjectivity and volatility of popular styles and techniques, it is also possible to elevate yourself above your competition and make a recognizable name or brand for yourself that will bring you income and influence of dizzying amounts.
Where to Start on the Web?
Anywhere. Seriously. Corral a hundred web folks into a room and talk to them. In addition to a case study for caffeine addiction, you'll find that there's a whole rainbow of where they started. Self taught, family business, college courses, Master's programs, and many times as a side-skill picked up in an unrelated job! That doesn't mean all these paths are equally easy or even possible for every person. The industry itself is always in flux as to what it's looking for.
I've seen a bias towards folks who are self-taught, or at least have extensive, hands on experience in the last couple of years. This is primarily due to the backlash against the growing generation of "Computer Science" college degree students who have developed INCREDIBLE skills... at Googling the most efficient method of solving the exact problem set before them. Am I downing on going to school for Comp. Sci.? Heck no. Some days I wish I had gone that route over my essentially unrelated Political Science degree. When a large enough number of job seekers, though, are giving the career path a bad name, it means that you have to work harder than before to overcome that stigma. As an example, I know a great guy that put in the work, and made the right connections, and got picked up by Microsoft immediately after undergrad graduation for a hefty sum. Again, there's hardly a 'wrong' path in such an open field.
So What Pays the Bills?
I've come to think of web, and general technology work, as collecting a toolbox. Sure, you're going to work for a company (or freelance, you self-starting go-getter!) that focuses on medical patient portals, or local restaurants, or e-commerce solutions. Utilizing niches is brilliant as a business move and is certainly where you'll turn a profit. What you should be building, personally, is your toolbox of awesome skills. HTML, CSS, Javascript. Photoshop, Illustrator, Color Theory. These are some of the generalized skills that underlie everything you will do. It's these exact same skills that build an order notification system for the pizza shop on the corner today, and re-haul the nation-wide Pizza Hut delivery back-end a few years down the road.
There's no, hidden, "new secret" you learn along the way. Polish your tools and combine them in new, interesting, sometimes frightening ways. Keep track of the stuff you find yourself using a lot, and catalog the dustier ones for when you'll inevitably need them again. As you work in a niche, get as good as you can at perfecting the skills that benefit your speed and quality there, but do not neglect the wider toolbox. The biggest way to dead-end yourself in the web industry is to stop being a web developer, and start being a local art gallery developer. Or a band page developer. Use the niche, but don't let it become you. This is as much a danger to freelancers as it is to developers on a full-time team.
How to Get From A to B
Work. Work hard. Whether you've gone through school, taught yourself, or even somehow rolled into a web career from somewhere tangentially related, grow at all costs. Set yourself up a website that showcases what you do. (See What Goes Into a Portfolio) Whether you officially freelance as a business or not, try to get involved in projects outside your bread-winner. Canvas neighborhood businesses, contact friends and family, get involved with a collaborative project group. Variety is the spice that will teach you skills you never dreamed of, as well as blow the minds of anyone reading your portfolio. Be able to tell them exactly what you did, and why it should impress them even more than it already has.
Using this combination of variety and a universal toolbox, you can position yourself to jump from freelancing local theater production pamphlets to designing visual branding as part of a business consulting firm. The sky's the limit. The biggest commodities in the labor market are good skills and, shockingly, labor itself. You can learn little industry foibles on the inside of a new team. Just show them that you've got the will to work hard and the universal tools to tackle anything with a bit of help, and you'll go far.