As someone once said, being employed gives you the illusion of security, while being self–employed gives you the illusion of freedom.
How to Get Started
Unless you have some savings to fall back on, the best way to make it as a self–employed web designer is to start by treating it as a paid hobby, and do the work during evenings and weekends, or part–time if your day job allows it. Once you are sure you are going to have enough work coming in, you can take the plunge.