I work through an agency now, so my typical client is a small or medium-size business that can’t hire or doesn’t need a full-time programmer or system admin. Usually they’ve been burned by outsourcing and gig sites and want someone who will take the time to understand their business, not just a coder who requires detailed specs and then beats them up with change orders.
I got my first freelancing gig more than ten years ago, while working f/t at an educational software company that was slowly going under. A friend I had worked with put me in touch with a friend of hers who had a successful web design/marketing agency, and he had clients who needed programming work (back end) that he couldn’t do. He started sending me work and then referred me to other design/marketing firms who needed the same kind of thing. If I was starting out today knowing what I know I would approach design/marketing agencies because they find the customers and frequently outsource anything beyond HTML/CSS or installing a Wordpress theme. Before long I connected with a company with a successful web-based business who had lost their developers (an outside firm that broke up and quit the client with short notice). I took that over. About the same time I gave a talk at a PHP user group about working with legacy code and got a job at the end when a guy who ran a non-profit approached me, telling me how his developer had quit and he had a long list of bugs and enhancements. I still work for both of those companies.
To get clients you need to tell everyone you know that you’re available, not get too fussy about what kind of work you do, focus on business requirements and needs rather than technology. Most important: listen to and communicate with your clients. The number one complaint I hear from my clients is that their last developer stopped returning calls and emails. Don’t pigeonhole yourself, recognize that languages and frameworks and tools are more alike than not, take on work that will push you a little. In the last couple of years I’ve gone from knowing nothing about AWS to managing cloud infrastructure for several companies, with some help from a friend who has a Linux/cloud security consulting practice.
My background is in enterprise logistics and business (accounting, payroll, AR/AP, etc.), so heavy on relational databases. I have worked in non-software businesses long enough to know the difference between a business problem or requirement and a technical problem. I don’t care much about languages or shiny new things, because my clients usually don’t. They want to fix bugs, reduce costs, increase revenue, scale their business. No business ever had the requirement “We need 2,000 more lines of Javascript code by next month” or “Let’s rewrite our web app with React because it’s cool.”