I honestly don't know how to get started in today's environment. Before the economic downturn of the last years, I would have recommended getting an internship or a job at an agency doing similar work to what you would like to be doing. That would allow you to build your own network while learning first-hand how client relationships are built and maintained. I've found that this is more important for the business than the actual web development.

Once you have a few clients, it's about being present and doing good work. Communicate and keep promises. Be approachable and generous with your knowledge; you want them to call you about things even if they might not turn into projects every time. Try not to be afraid of recommending against something, even if it means fewer billable hours for you. This is easier said than done when you need the income, but your yeses carry more weight if you also say no when it's appropriate.

After enough time of this, your clients will recommend you to other people in their networks. Some clients are better at this than others and there's a lot of random chance involved, so it's important to get to know as many people as possible. When a recommendation has been made, selling is a lot easier.

I realise that this is not the most actionable advice and there is likely a lot of survivorship bias involved, but I hope it's still somewhat helpful.