This is actually the best advice. It is how I started and I have have a job because of a similar method. I would advise you to build up yourself a nice portfolio - Spend time on this, nurture it as if it's your baby. It will do all the magic and show your clients what you are and what you're made of. Once you have this up and running it's time to try find some references. You may need to start at a low price - believe me we have all been there, but the more items you have down on your portfolio the better it looks, eventually more jobs will come and potentially bigger ones at that.
Everyone has to start somewhere - build yourself from the ground up and keep adding stuff to your portfolio. Also try to blog and write good content, if people browsing your portfolio see a blog and also notice you are very keen and have a passion, people love that kind of stuff.
Where to find work you are probably asking yourself? Your best bet is to google web design freelance jobs, it is going to be a tough cookie getting your first job on a freelance website with small credentials, I remember trying to get my first job on one, it was tough. But in the end I got there, it's good writing a good cover letter when applying to freelance jobs, show them how passionate you are about web design and how really are the person for the job. When I got my first freelance job I was over the moon, quite literally! But once the first comes in, it gets a whole lot easier. Some clients come back for more, maintenance for their website etc.
About your experience, I wouldn't worry about that. Web Design is a weird one, I have read all kinds of articles of how people have gone off to University etc doing degrees in all kinds of stuff non-related to web design and then go off and do some freelance build up a portfolio and when they are ready they go out and apply to a company and get the job. The truth is about web design, you get the most experience and understanding on the job and most of the time that is by reading blogs, tutorials and community websites like SitePoint.
At the end of the day! Don't give up, keep going at freelance websites and applying for projects. It will all come in time
tr;dr - Get a portfolio, find jobs on the cheap, add to portfolio, apply to more freelance websites, find a job at the end of it all when you're ready.